- “New Tool Hides Data In Plain Sight On HDDs” (SlashDot; 2011.04.25) – http://it.slashdot.org/story/11/04/25/1558237/New-Tool-Hides-Data-In-Plain-Sight-On-HDDs
*“A group of researchers has developed a new application that can hide sensitive data on a hard drive without encrypting it or leaving any obvious signs that the data is present. The new steganography system relies on the old principle of hiding valuables in plain sight. Developed by a group of academic researchers in the US and Pakistan, the system can be used to embed secret data in existing structures on a given HDD by taking advantage of the way file systems are designed and implemented. The software does this by breaking a file to be hidden into a number of fragments and placing the individual pieces in clusters scattered around the hard drive.”*- “Researchers Propose New Steganography System for Hiding Data” by Dennis Fisher (Threat Post)- https://threatpost.com/en_us/blogs/researchers-propose-new-steganography-system-hiding-data-042511
- “Designing a cluster-based covert channel to evade disk investigation and forensic” by Hassan Khana, Mobin Javedb, Syed Ali Khayamb and Fauzan Mirzab – http://www.sciencedirect.com/

- “Researchers Propose New Steganography System for Hiding Data” by Dennis Fisher (Threat Post)- https://threatpost.com/en_us/blogs/researchers-propose-new-steganography-system-hiding-data-042511

## 2011.04.25

### Steganography

### Electronic Music

- Wolfram tones – http://tones.wolfram.com/
- “If Music Be Thy Dream Of Filthy Lucre, Press Stop” by Jon Evans (Tech Crunch; 2011.04.24) – http://techcrunch.com/2011/04/24/if-music-be-thy-dream/

- “Space Music: Gary Numan, Asperger Syndrome and Roswell Return” (Discovery news; 2011.03.10) – http://news.discovery.com/space/space-music-gary-numan-asperger-syndrome-and-roswell-return.html
- “Praying to the Aliens: Gary Numan (Aliens, alienation and Asperger’s Syndrome)” by Etienne Gilfillan (ForteanTimes; 2010.11) – http://www.forteantimes.com/features/interviews/4693/praying_to_the_aliens_gary_numan.html
- “Bodytonic Podcast 101: Roswell Return” – http://www.bodytonicmusic.com/podcasts/2011/mar/04/bodytonic-podcast-101-roswell-return/
- “The Astronaut’s Playlist: Groovy Songs for Space Travelers” by Tom Chao (SPACE.com; 2011.03.06) – http://www.space.com/11037-space-music-playlist-astronauts-wakeup.html

- “Triumph of the Cyborg Composer (David Cope’s software creates beautiful, original music. Why are people so angry about that?)” by Ryan Blitstein (Miller-McCune; 2011.2.22) – http://www.miller-mccune.com/culture-society/triumph-of-the-cyborg-composer-8507/

Related at this blog: Music scores, tabs, … – https://eikonal.wordpress.com/2011/02/23/music-scores-tabs/ | Gypsy music – https://eikonal.wordpress.com/2011/01/05/gypsy-music/ | Psychodelic rock from 1970s – https://eikonal.wordpress.com/2010/07/12/psychodelic-rock-from-1970s/ | Streaming and other free music online – https://eikonal.wordpress.com/2010/01/04/streaming-and-other-free-music-online/

### Cloud computing

- “Cloud development: 9 gotchas to know before you jump in” by Bob Violino (ComputerWorld; 2011.04.25) – http://www.computerworld.com/s/article/9216124/Cloud_development_9_gotchas_to_know_before_you_jump_in?source=rss_news

## Online storage

- YouSendIt – https://www.yousendit.com/
- TransferBigFiles – https://www.transferbigfiles.com/
- Dropbox – http://www.dropbox.com/
- “The Cleverest Ways to Use Dropbox That You’re Not Using” (Lifehacker) – http://lifehacker.com/5527055/the-cleverest-ways-to-use-dropbox-that-youre-not-using
- “Use Dropbox for More Than Just File Syncing” – http://lifehacker.com/5358983/use-dropbox-for-more-than-just-file-syncing

Security problems:

- “Dropbox Caught With Its Finger in the Cloud Cookie Jar” by Woody Leonhard (Infoworld; 2011.05.16) – http://www.pcworld.com/article/227999/dropbox_caught_with_its_finger_in_the_cloud_cookie_jar.html | http://www.infoworld.com/t/data-security/dropbox-caught-its-finger-in-the-cloud-cookie-jar-179?source=footer –
*Online file storage and sharing site Dropbox admits that it can see the data you’ve stored. Oops…* - “Dropbox Lied to Users About Data Security, Complaint to FTC Alleges” by Ryan Singel (Wired; 2011.05.13) – http://www.wired.com/threatlevel/2011/05/dropbox-ftc/
- “How Dropbox sacrifices user privacy for cost savings” by Christopher Soghoian (“slight paranois” blog; 2011.04.12) – http://paranoia.dubfire.net/2011/04/how-dropbox-sacrifices-user-privacy-for.html
*Dropbox, the popular cloud based backup service deduplicates the files that its users have stored online. This means that if two different users store the same file in their respective accounts, Dropbox will only actually store a single copy of the file on its servers.* - “Why I switched from Dropbox to Windows Live Mesh” by Ed Bott (ZDNet; 2011.07.04) – http://www.zdnet.com/blog/bott/why-i-switched-from-dropbox-to-windows-live-mesh/3512
- Due to recent security problems and their bad policy about user data, you must pre-encrypt yall your data that you store in your Dropbox cabinet. TrueCrypt is one good offline encrypter: Dropbox TipsAndTricks > Truecrypt – http://wiki.dropbox.com/TipsAndTricks/Truecrypt
- “How To Add a Second Layer of Encryption to Dropbox [Updated]” by Melanie Pinola (Lifehacker) – http://lifehacker.com/5794486/how-to-add-a-second-layer-of-encryption-to-dropbox
- Dropbox portable: http://forums.dropbox.com/topic.php?id=33387

- Microsoft’s SkyDrive – http://skydrive.live.com/ – another online free drive storage [up to 25GB] – requires Hotmail account.
- use og GMail as the online disk:
- GMail Drive shell extension – http://www.viksoe.dk/code/gmail.htm

Related here: Cloud security – https://eikonal.wordpress.com/2010/08/09/cloud-security/ | Virtualization Tools – https://eikonal.wordpress.com/2010/12/02/virtualization-tools/ | Virtualization security – https://eikonal.wordpress.com/2010/08/09/virtualization-security/ | Threats of cloud computing – https://eikonal.wordpress.com/2010/02/03/threats-of-cloud-computing/.

## 2011.04.21

### Gut bacteria, second brain, etc

- “Your Gut, Your Brain, and Economics – Should Economists Considers Gut-Brain Communication?” by Daniel R. Hawes (Psychology Today; 2011.08.02) – http://www.psychologytoday.com/blog/quilted-science/201108/your-gut-your-brain-and-economics
- “Gut flora: You are what your bacteria eat” by Neil Katz (CBS News; 2011.04.21) – http://www.cbsnews.com/8301-504763_162-20056028-10391704.html
- “Scientist Find Gut Bacteria Divides People Into Three Types” (FOX News; 2011.04.21) – http://www.myfoxhouston.com/dpps/health/scientist-find-gut-bacteria-divides-people-into-three-types-dpgoha-20110421-fc_12862614

- “Bacteria Divide People Into 3 Types, Scientists Say” by Carl Zimmer (NYTimes; 2011.04.20) – http://www.nytimes.com/2011/04/21/science/21gut.html
- Enterotype 1:
- produces more enzymes for making vitamin B7 (also known as biotin).
- high levels of bacteria called Bacteroides

- Enterotype 2:
- produces more enzymes for vitamin B1 (thiamine).
- Bacteroides were relatively rare, while the genus Prevotella was unusually common.

- Enterotype 3

- Enterotype 1:
- “Enterotypes of the human gut microbiome” (Nature; 2011.04.20?) – http://www.nature.com/nature/journal/vaop/ncurrent/full/nature09944.html
- Abstract:

*Our knowledge of species and functional composition of the human gut microbiome is rapidly increasing, but it is still based on very few cohorts and little is known about variation across the world. By combining 22 newly sequenced faecal metagenomes of individuals from four countries with previously published data sets, here we identify three robust clusters (referred to as enterotypes hereafter) that are not nation or continent specific. We also confirmed the enterotypes in two published, larger cohorts, indicating that intestinal microbiota variation is generally stratified, not continuous. This indicates further the existence of a limited number of well-balanced host–microbial symbiotic states that might respond differently to diet and drug intake. The enterotypes are mostly driven by species composition, but abundant molecular functions are not necessarily provided by abundant species, highlighting the importance of a functional analysis to understand microbial communities. Although individual host properties such as body mass index, age, or gender cannot explain the observed enterotypes, data-driven marker genes or functional modules can be identified for each of these host properties. For example, twelve genes significantly correlate with age and three functional modules with the body mass index, hinting at a diagnostic potential of microbial markers.* - “How Microbes Defend and Define Us” by Carl Zimmer (NYTimes; 2010.07.12) – http://www.nytimes.com/2010/07/13/science/13micro.html

- “A human gut microbial gene catalogue established by metagenomic sequencing” (Nature; 2010.03.04) – http://www.nature.com/nature/journal/v464/n7285/full/nature08821.html

### Geotracking and surveillance

## And everyone else (and his dog) is on the game, too …

- http://yro.slashdot.org/story/11/05/02/1724231/Tom-Tom-Sells-GPS-Info-To-Dutch-Cops
*“As smartphones with GPS capabilities wear away at the dedicated GPS market, vendors like Tom Tom need to find new revenue streams. Tom Tom decided it would be a good idea to ‘share’ (i.e., sell) aggregated data from their users*to Dutch law enforcement. The company claims they assumed that the data would be used to improve traffic safety and road engineering, and were shocked, shocked to discover that instead the police used it to figure out the best places to put speed traps.” - “Tom Tom’s sleazy way to make up GPS revenue shortfall” by Chris Nerey (IT World; 2011.04.29) – http://www.itworld.com/mobile-wireless/160861/tom-toms-sleazy-way-make-gps-revenue-shortfall
- …

*TomTom NV, Europe’s largest navigation device maker, went into damage control mode Wednesday after it emerged that Dutch police have been using data collected from drivers who use the company’s products to set speed traps.**Earlier, TomTom had reported weak first quarter earnings in which it cut 2011 sales forecasts and said it was seeking to compensate for a decline in demand for personal navigation devices by growing service revenues, including selling traffic data to governments.*… - “GPS Maker TomTom Submits Your Speed Data To Police” (SlashDot; 2011.04.28) – http://yro.slashdot.org/story/11/04/28/1719247/GPS-Maker-TomTom-Submits-Your-Speed-Data-To-Police
*“The GPS systems in TomTom’s Live range all feature built-in 3G data cards, which feed location and route information back to a central server. According to CNET, this data, along with users’ speed information, is being made available to local governments and the police.”*

From the article: “Knowing the cops can see where you’re driving and how fast you’re going is eye-opening stuff, but TomTom says the data is anonymous and can never be traced back to an individual user or device. Ordinarily, we’d be reassured by this, but we recall Apple saying something similar before the location-tracking excrement hit the phone-carrying fan.” - “TomTom admits to sending your routes and speed information to the police” by Rory Reid (CNET UK; 2011.04.28) – http://crave.cnet.co.uk/cartech/tomtom-admits-to-sending-your-routes-and-speed-information-to-the-police-50003618/
- …

*The sat-navs in TomTom’s Live range all feature built-in 3G data cards, which feed location and route information back to a central server, which allows TomTom to create a map of congestion hotspots. It’s now emerged that this data, however, along with a user’s speed, is being made available to local governments and authorities.*TomTom CEO Harold Goddijn revealed the information on the company’s website. “We are now aware that the police have used traffic information that you have helped to create to place speed cameras at dangerous locations where the average speed is higher than the legally allowed speed limit,” he says.

*Knowing the cops can see where you’re driving and how fast you’re going is eye-opening stuff, but TomTom says the data is anonymous and can never be traced back to an individual user or device. Ordinarily, we’d be reassured by this, but we recall Apple saying something similar before the location-tracking excrement hit the phone-carrying fan.*… - “TomTom admits police used data for speed traps” by Toby Sterling (Forbed/AP; 2011.04.27) – http://www.forbes.com/feeds/ap/2011/04/27/business-telecommunications-equipment-eu-netherlands-earns-tomtom_8438128.html

## Androids, too …

- “Your Location ‘Extremely Valuable’ To Google” (SlashDot; 2011.05.02) – http://tech.slashdot.org/story/11/05/02/0438206/Your-Location-Extremely-Valuable-To-Google
- “Your location ‘extremely valuable’ to Google” (International Business Times; 2011.05.01) – http://www.ibtimes.com/articles/139985/20110501/your-location-extremely-valuable-to-google.htm
*… Then, just weeks ago Los Angeles-based researcher Samy Kamkar illustrated that Google Android based smartphones were sending precise GPS location and other data back to Google “several times an hour.”*…

*… The company is using this information to create a digital databases that include the physical location of hundreds of millions of Wi-Fi access points. Smartphones use those databases as a kind of electronic map to chart their own location.*…*… Moreover, beyond improving services like maps for end-users, it also positions the company in front a fast-growing location-based advertising market.*…

*… The problem, however, is if the data fall into the wrong hands, or if the data is compromised.*…

*… The data is precise enough that Kamkar says Google can correlate timing and frequency of phone usage to pinpoint an Android owner’s home address.**…*

*… “If your phone is at the same location during night hours, they know where you live,” says Kamkar. “If your phone location is on the move, they can guess that you’re in a car and even calculate how fast your car is moving.”*…

- “Your location ‘extremely valuable’ to Google” (International Business Times; 2011.05.01) – http://www.ibtimes.com/articles/139985/20110501/your-location-extremely-valuable-to-google.htm
- “Google Defends Way It Gets Phone Data” by Jennifer Valentino-DeVries (The Wall Street Journal; 2011.04.23) – http://online.wsj.com/article/SB10001424052748703387904576279451001593760.html
- “Apple, Google Collect User Data” by Jennifer Valentino-DeVries (The Wall Street Journal; 2011.04.22) – http://online.wsj.com/article/SB10001424052748703983704576277101723453610.html
- packetlss – Android location service cache dumper – https://github.com/packetlss/android-locdump
- “Android phones keep location cache, too, but it’s harder to access” by Chris Foresman (Ars Technica; 2011.04.22) – http://arstechnica.com/gadgets/news/2011/04/android-phones-keep-location-cache-too-but-its-harder-to-access.ars
- “Android Phones Track Users Locations, Just LIke iPhones” by Jesse Emspak (International Business Times; 2011.04.21) – http://www.ibtimes.com/articles/137143/20110421/android-phones-track-users-movements.htm

## iPhone doing surveilance, on whose behalf?

- “IPhone Stored Location in Test Even if Disabled” by Jennifer Valentino-DeVries (The Wall Street Journal; 2011.04.25) – http://online.wsj.com/article/SB10001424052748704123204576283580249161342.html
- “Why you should care about the iPhone location-tracking issue” by Brian X. Chen and Mike Isaac (WIRED; 2011.04.25?) – http://www.cnn.com/2011/TECH/mobile/04/25/iphone.tracking.wired/
- “The scoop: Apple’s iPhone is NOT storing your accurate location, and NOT storing history” by Peter Batty (geothought blog; 2011.04.24) – http://geothought.blogspot.com/2011/04/scoop-apples-iphone-is-not-storing-your.html
- “The Week in Tweets: Your iPhone Is Watching You” by Sara Yin (PC Magazine; 2011.04.25) – http://www.pcmag.com/slideshow/story/263506/The-Week-in-Tweets:-Your-iPhone-Is-Watching-You
- “3 Major Issues with the Latest iPhone Tracking “Discovery”” by Alex Levison (at his blog; 2011.04.21) – https://alexlevinson.wordpress.com/2011/04/21/3-major-issues-with-the-latest-iphone-tracking-discovery/
- 1) Apple is not collecting this data.
- 2) This hidden file is neither new nor secret.
- 3) This “discovery” was published months ago.

- “So What If iPhones Spy User Locations” by George Hulme (Information Week; 2011.04.21) – http://www.informationweek.com/news/security/privacy/229402104
*And, it appears, phones based on the Android operating system do the same thing, essentially. The location information is stored in files named cache.cell and cache.wifi.* - “iPhone Location Tracking Brouhaha in Perspective + Personal Status Note” by Lauren Weinstein (Lauren Weinstein’s Blog; 2011.04.21) – http://lauren.vortex.com/archive/000843.html
*Some observers (many of whom seem to be rather hardcore Apple “fanboys”), appear to be attempting to minimize the seriousness of this situation, suggesting that it really isn’t a big deal since Apple reportedly isn’t routinely sending the collected location data to their own servers — some apologists even parroting the tired and dangerous meme that “if you aren’t doing anything wrong you have nothing to fear from such data being gathered.”*

There’s also considerable speculation regarding the whys and wherefores behind Apple’s deploying this data mechanism.

None of this substantively changes the bottom line.

This isn’t rocket science. The collection of this data on these devices, especially in unencrypted form, is incredibly dangerous, stupid, and disrespectful of Apple’s customers.

In an age when U.S. Customs and now even local police departments are claiming the right to use specialized equipment to drain smartphones and laptops of their stored data without any kind of warrants or court orders, the presence of such comprehensive location data in these devices represents a treasure trove for everything from completely unreasonable law enforcement “fishing expeditions” to aggressive and nosy divorce attorneys. - “Researchers say iPhones can track users’ movements” 9BBC news; 2011.04.21) – http://www.bbc.co.uk/news/technology-13162893
- “Why and How Apple Is Collecting Your iPhone Location Data” by Brian X. Chen (WIRED; 2011.04.21) – http://www.wired.com/gadgetlab/2011/04/apple-iphone-tracking
- “What Your iPhone Knows About You” by Jennifer Valentino-DeVries (The Wall Street Journal; 2011.04.20) – http://blogs.wsj.com/digits/2011/04/20/what-your-iphone-knows-about-you
- “Got an iPhone or 3G iPad? Apple is recording your moves” by Alasdair Allan (O’Reilly Radar; 2011.04.20) – http://radar.oreilly.com/2011/04/apple-location-tracking.html – A hidden file in iOS 4 is regularly recording the position of devices.
- “iPhone Tracks Your Every Move, and There’s a Map for That” by Brian X. Chen (Wired; 2011.04.20) – http://www.wired.com/gadgetlab/2011/04/iphone-tracks/
- “Report: iPhones secretly track their users’ locations” by John D. Sutter (CNN Tech; 2011.04) – http://www.cnn.com/2011/TECH/mobile/04/20/iphone.tracking/
*The unauthorized surveillance started in June 2010, when the latest version of Apple’s mobile operating system was released, according to two researchers who say they discovered a hidden tracking file and posted it out of concern for users.* - “iPhones Secretly Track Your Every Move, Researchers Say” by Catharine Smith (The Huffington Post; 201.04.20) – http://www.huffingtonpost.com/2011/04/20/apple-iphones-tracking-users_n_851532.html
*According to The Guardian, Warden and Allan discovered that devices running iOS 4 keep a record of time-stamped coordinates in a file called “consolidated.db.”* - “Apple Users, Beware: iPhones Secretly Tracking Location, Experts Warn” by Maxim Lott (Fox News; 2011.04.20) – http://www.foxnews.com/scitech/2011/04/20/apple-iphone-users-beware-location-tracking/
- “Got an iPhone or 3G iPad? Apple is recording your moves” by Alasdair Allan (O’Reilly Radar; 2011.04.20) – http://radar.oreilly.com/2011/04/apple-location-tracking.html –
*A hidden file in iOS 4 is regularly recording the position of devices.* - “iPhone keeps record of everywhere you go” by Charles Arthur (Guardian; 2011.04.20) – http://www.guardian.co.uk/technology/2011/apr/20/iphone-tracking-prompts-privacy-fears
- iPhone Tracker – http://petewarden.github.com/iPhoneTracker/

Old and unrelated (or, is it?):

- The Snitch in Your Pocket (Law enforcement is tracking Americans’ cell phones in real time—without the benefit of a warrant), by Michael Isikoff (NEWSWEEK; Feb 19, 2010.02.19; from the magazine issue dated 2010.03.01): http://www.newsweek.com/id/233916

Related: Geolocation – https://eikonal.wordpress.com/2011/04/08/geolocation/

*
*

## 2011.04.18

### PT-Quantum Mechanics

- Carl Bender’s speaches at PIRSA (Perimeter Institute Recorded Seminar Archive) – http://pirsa.org/index.php?p=speaker&name=Carl_Bender
- Carl Bender’s talk on turbulence, iterated maps, chaos and classical mechanics in classical domain. Includes several interesting experimental demonstrations. – http://artsci.wustl.edu/~spenteco/newVideo/DLP_bender_083109.html
- Carl Bender’s papers at arXiv – http://arxiv.org/find/quant-ph/1/au:+Bender_C/0/1/0/all/0/1
- “Response to Shalaby’s Comment on “Families of Particles with Different Masses in PT-Symmetric Quantum Field Theory”” by Carl M. Bender, S. P. Klevansky (arXiv:1103.0338; 2011.03.02) – http://arxiv.org/abs/1103.0338
- Abstract:

*In a recent Comment [arXiv: 1101.3980] Shalaby criticised our paper “Families of Particles with Different Masses in PT-Symmetric Quantum Field Theory” [arXiv:1002.3253]. On examining his arguments, we find that there are serious flaws at almost every stage of his Comment. In view of space and time considerations, we point out the major flaws that render his arguments invalid. Essentially Shalaby is attempting to obtain our results from a variational principle and to find a physical interpretation of his calculation. The variational procedure that he uses is inapplicable, and his description of the physics is wrong. We thus refute his criticism on all levels.* - “PT-symmetric quantum state discrimination” by Carl M. Bender, Dorje C. Brody, Joao Caldeira, Bernard K. Meister (arXiv:1011.1871; 2010.11.08) – http://arxiv.org/abs/1011.1871
- Abstract:

*Suppose that a system is known to be in one of two quantum states, or . If these states are not orthogonal, then in conventional quantum mechanics it is impossible with one measurement to determine with certainty which state the system is in. However, because a non-Hermitian PT-symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states, it is always possible to choose this inner product so that the two states and are orthogonal. Thus, quantum state discrimination can, in principle, be achieved with a single measurement.* - “Tunneling in classical mechanics” by Carl M. Bender, Daniel W. Hook (arXiv:1011.0121; 2010.09.16) – http://arxiv.org/abs/1011.0121
- Abstract:

*A classical particle that is initially in a classically allowed region of a potential is not confined to this region for all time if its energy is complex. Rather, the particle may travel through complex coordinate space and visit other classically allowed regions. Thus, a complex-energy classical particle can exhibit tunneling-like behavior. This tunneling behavior persists as the imaginary part of the energy tends to zero. Hence one may compare complex classical tunneling times with quantum tunneling probabilities. An accurate numerical study of quantum and classical tunneling demonstrates that as the energy increases, the probabilities associated with complex classical tunneling approach the corresponding quantum probabilities.*- The Hamiltonian with the potential has following lowest energy levels:
- ,
- ,
- ,
- ,
- .
- lies just above the barrier separating two potential wells.

- The sextic potential has following lowest energy levels:
- ,
- ,
- ,
- .

- The geometric charactericts of the quartic potential are:
- the left well minimum is at ;
- the right well minimum is at ;
- the barrier is at

- The geometric charactericts of the sextic potential are:
- the left well minimum is at ;
- the right well minimum is at ;
- the barrier is at

- The Hamiltonian with the potential has following lowest energy levels:
- “Extending PT symmetry from Heisenberg algebra to E2 algebra” by Carl M. Bender, R. J. Kalveks (arXiv:1009.3236 2010.09.16; Int.J.Theor.Phys.50:955-962,2011) – http://arxiv.org/abs/1009.3236
- Abstract:

*The E2 algebra has three elements, J, u, and v, which satisfy the commutation relations . We can construct the Hamiltonian , where g is a real parameter, from these elements. This Hamiltonian is Hermitian and consequently it has real eigenvalues. However, we can also construct the PT-symmetric and non-Hermitian Hamiltonian , where again g is real. As in the case of PT-symmetric Hamiltonians constructed from the elements x and p of the Heisenberg algebra, there are two regions in parameter space for this PT-symmetric Hamiltonian, a region of unbroken PT symmetry in which all the eigenvalues are real and a region of broken PT symmetry in which some of the eigenvalues are complex. The two regions are separated by a critical value of g.* - “Quantum counterpart of spontaneously broken classical PT symmetry” by Carl M. Bender, Hugh F. Jones (arXiv:1008.0782 2010.08.04; J.Phys.A44:015301,2011) – http://arxiv.org/abs/1008.0782
- Abstract:

*The classical trajectories of a particle governed by the PT-symmetric Hamiltonian () have been studied in depth. It is known that almost all trajectories that begin at a classical turning point oscillate periodically between this turning point and the corresponding PT-symmetric turning point. It is also known that there are regions in for which the periods of these orbits vary rapidly as functions of and that in these regions there are isolated values of for which the classical trajectories exhibit spontaneously broken PT symmetry. The current paper examines the corresponding quantum-mechanical systems. The eigenvalues of these quantum systems exhibit characteristic behaviors that are correlated with those of the associated classical system.* - “Almost zero-dimensional PT-symmetric quantum field theories” by Carl M. Bender (arXiv:1003.3881; 2010.03.19) – http://arxiv.org/abs/1003.3881
- Abstract:

*In 1992 Bender, Boettcher, and Lipatov proposed in two papers a new and unusual nonperturbative calculational tool in quantum field theory. The objective was to expand the Green’s functions of the quantum field theory as Taylor series in powers of the space-time dimension D. In particular, the vacuum energy for a massless \phi^{2N} (N=1,2,3,…) quantum field theory was studied. The first two Taylor coefficients in this dimensional expansion were calculated {\it exactly} and a set of graphical rules were devised that could be used to calculate approximately the higher coefficients in the series. This approach is mathematically valid and gives accurate results, but it has not been actively pursued and investigated. Subsequently, in 1998 Bender and Boettcher discovered that PT-symmetric quantum-mechanical Hamiltonians of the form H=p^2+x^2(ix)^\epsilon, where \epsilon\geq0, have real spectra. These new kinds of complex non-Dirac-Hermitian Hamiltonians define physically acceptable quantum-mechanical theories. This result in quantum mechanics suggests that the corresponding non-Dirac-Hermitian D-dimensional \phi^2(i\phi)^\epsilon quantum field theories might also have real spectra. To examine this hypothesis, we return to the technique devised in 1992 and in this paper we calculate the first two coefficients in the dimensional expansion of the ground-state energy of this complex non-Dirac-Hermitian quantum field theory. We show that to first order in this dimensional approximation the ground-state energy is indeed real for \epsilon\geq0.* - “Families of particles with different masses in PT-symmetric quantum field theory” by C. M. Bender, S. P. Klevansky (arXiv:1002.3253; 2010.07.05) – http://arxiv.org/abs/1002.3253
- Abstract:

*An elementary field-theoretic mechanism is proposed that allows one Lagrangian to describe a family of particles having different masses but otherwise similar physical properties. The mechanism relies on the observation that the Dyson-Schwinger equations derived from a Lagrangian can have many different but equally valid solutions. Nonunique solutions to the Dyson-Schwinger equations arise when the functional integral for the Green’s functions of the quantum field theory converges in different pairs of Stokes’ wedges in complex field space, and the solutions are physically viable if the pairs of Stokes’ wedges are PT symmetric.* - “Classical Particle in a Complex Elliptic Potential” by Carl M. Bender, Daniel W. Hook, Karta Singh Kooner (arXiv:1001.1548 2010.01.10; J.Phys.A43:165201,2010) – http://arxiv.org/abs/1001.1548
- Abstract:

*This paper reports a numerical study of complex classical trajectories of a particle in an elliptic potential. This study of doubly-periodic potentials is a natural sequel to earlier work on complex classical trajectories in trigonometric potentials. For elliptic potentials there is a two-dimensional array of identical cells in the complex plane, and each cell contains a pair of turning points. The particle can travel both horizontally and vertically as it visits these cells, and sometimes the particle is captured temporarily by a pair of turning points. If the particle’s energy lies in a conduction band, the particle drifts through the lattice of cells and is never captured by the same pair of turning points more than once. However, if the energy of the particle is not in a conduction band, the particle can return to previously visited cells.* - “Complex Elliptic Pendulum” by Carl M. Bender, Daniel W. Hook, Karta Kooner (arXiv:1001.0131; 2009.12.31) – http://arxiv.org/abs/1001.0131
- Abstract:

*This paper briefly summarizes previous work on complex classical mechanics and its relation to quantum mechanics. It then introduces a previously unstudied area of research involving the complex particle trajectories associated with elliptic potentials.* - “Probability Density in the Complex Plane” by Carl M. Bender, Daniel W. Hook, Peter N. Meisinger, Qing-hai Wang (arXiv:0912.4659; 2010.01.23) – http://arxiv.org/abs/0912.4659
- Abstract:

*The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years many papers have been published on the extension of both quantum mechanics and classical mechanics into the complex domain. However, the question of whether complex quantum mechanics resembles complex classical mechanics at high energy has not yet been studied. This paper introduces the concept of a local quantum probability density $\rho(z)$ in the complex plane. It is shown that there exist infinitely many complex contours of infinite length on which is real and positive. Furthermore, the probability integral is finite. Demonstrating the existence of such contours is the essential element in establishing the correspondence between complex quantum and classical mechanics. The mathematics needed to analyze these contours is subtle and involves the use of asymptotics beyond all orders.* - “Complex Correspondence Principle” by Carl M. Bender, Daniel W. Hook, Peter N. Meisinger, Qing-hai Wang (arXiv:0912.2069 2009.12.10; Phys.Rev.Lett.104:061601,2010) – http://arxiv.org/abs/0912.2069
- Abstract:

*Quantum mechanics and classical mechanics are two very different theories, but the correspondence principle states that quantum particles behave classically in the limit of high quantum number. In recent years much research has been done on extending both quantum mechanics and classical mechanics into the complex domain. This letter shows that these complex extensions continue to exhibit a correspondence, and that this correspondence becomes more pronounced in the complex domain. The association between complex quantum mechanics and complex classical mechanics is subtle and demonstrating this relationship prequires the use of asymptotics beyond all orders.* - “PT symmetry and necessary and sufficient conditions for the reality of energy eigenvalues” by Carl M. Bender, Philip D. Mannheim (arXiv:0902.1365; 2009.02.09) – http://arxiv.org/abs/0902.1365
- Abstract:

*Despite its common use in quantum theory, the mathematical requirement of Dirac Hermiticity of a Hamiltonian is sufficient to guarantee the reality of energy eigenvalues but not necessary. By establishing three theorems, this paper gives physical conditions that are both necessary and sufficient. First, it is shown that if the secular equation is real, the Hamiltonian is necessarily PT symmetric. Second, if a linear operator C that obeys the two equations [C,H]=0 and C^2=1 is introduced, then the energy eigenvalues of a PT-symmetric Hamiltonian that is diagonalizable are real only if this C operator commutes with PT. Third, the energy eigenvalues of PT-symmetric Hamiltonians having a nondiagonalizable, Jordan-block form are real. These theorems hold for matrix Hamiltonians of any dimensionality.* - “Optimal Time Evolution for Hermitian and Non-Hermitian Hamiltonians” by Carl M. Bender, Dorje C. Brody (arXiv:0808.1823; 2008.08.13) – http://arxiv.org/abs/0808.1823
- Abstract:

*Consider the set of all Hamiltonians whose largest and smallest energy eigenvalues, E_max and E_min, differ by a fixed energy \omega. Given two quantum states, an initial state |\psi_I> and a final state |\psi_F>, there exist many Hamiltonians H belonging to this set under which |\psi_I> evolves in time into |\psi_F>. Which Hamiltonian transforms the initial state to the final state in the least possible time \tau? For Hermitian Hamiltonians, has a nonzero lower bound. However, among complex non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, \tau can be made arbitrarily small without violating the time-energy uncertainty principle. The minimum value of \tau can be made arbitrarily small because for PT-symmetric Hamiltonians the evolution path from the vector |\psi_I> to the vector |\psi_F>, as measured using the Hilbert-space metric appropriate for this theory, can be made arbitrarily short. The mechanism described here resembles the effect in general relativity in which two space-time points can be made arbitrarily close if they are connected by a wormhole. This result may have applications in quantum computing.* - “Quantum effects in classical systems having complex energy” by Carl M. Bender, Dorje C. Brody, Daniel W. Hook (arXiv:0804.4169 2008.04.25; J.Phys.A41:352003,2008) – http://arxiv.org/abs/0804.4169
- Abstract:

*On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems extended into the complex domain. Three models are examined: the quartic double-well potential , the cubic potential , and the periodic potential . For the quartic potential a wave packet that is initially localized in one side of the double-well can tunnel to the other side. Complex solutions to the classical equations of motion exhibit a remarkably analogous behavior. Furthermore, classical solutions come in two varieties, which resemble the even-parity and odd-parity quantum-mechanical bound states. For the cubic potential, a quantum wave packet that is initially in the quadratic portion of the potential near the origin will tunnel through the barrier and give rise to a probability current that flows out to infinity. The complex solutions to the corresponding classical equations of motion exhibit strongly analogous behavior. For the periodic potential a quantum particle whose energy lies between -1 and 1 can tunnel repeatedly between adjacent classically allowed regions and thus execute a localized random walk as it hops from region to region. Furthermore, if the energy of the quantum particle lies in a conduction band, then the particle delocalizes and drifts freely through the periodic potential. A classical particle having complex energy executes a qualitatively analogous local random walk, and there exists a narrow energy band for which the classical particle becomes delocalized and moves freely through the potential.* - “Comment on the Quantum Brachistochrone Problem” by C. M. Bender, D. C. Brody, H. F. Jones, B. K. Meister (arXiv:0804.3487; 2008.04.22) – http://arxiv.org/abs/0804.3487
- Abstract:

*In this brief comment we attempt to clarify the apparent discrepancy between the papers [1] and [2] on the quantum brachistochrone, namely whether it is possible to use a judicious mixture of Hermitian and non-Hermitian quantum mechanics to evade the standard lower limit on the time taken for evolution by a Hermitian Hamiltonian with given energy dispersion between two given states.* - “Exact Isospectral Pairs of PT-Symmetric Hamiltonians” by Carl M. Bender, Daniel W. Hook (arXiv:0802.2910 2008.04.27; J.Phys.A41:244005,2008) – http://arxiv.org/abs/0802.2910
- Abstract:
*A technique for constructing an infinite tower of pairs of PT-symmetric Hamiltonians, and (n=2,3,4,…), that have exactly the same eigenvalues is described. The eigenvalue problem for the first Hamiltonian of the pair must be posed in the complex domain, so its eigenfunctions satisfy a complex differential equation and fulfill homogeneous boundary conditions in Stokes’ wedges in the complex plane. The eigenfunctions of the second Hamiltonian of the pair obey a real differential equation and satisfy boundary conditions on the real axis. This equivalence constitutes a proof that the eigenvalues of both Hamiltonians are real. Although the eigenvalue differential equation associated with is real, the Hamiltonian exhibits quantum anomalies (terms proportional to powers of ). These anomalies are remnants of the complex nature of the equivalent Hamiltonian . In the classical limit in which the anomaly terms in are discarded, the pair of Hamiltonians and have closed classical orbits whose periods are identical.* - Extracts:
- Paper considers the first three members of the family of PT-symmetric Hamiltonians for and . Each of these Hamiltonians has the same discrete real spectrum as a corresponding member of another family of Hamiltonians which are Hermitian.
- Example : For one gets . Notice the quantum-anomaly term (proportional to ). The corresponding classical Hamiltonians and also have a correspondence between them: namely, each closed orbit of first one has a corresponding closed orbit of the second one, both orbits with the exactly same periods.
- Example :
- .
- .

- Example :
- .
- .

- Abstract:
- “Does the complex deformation of the Riemann equation exhibit shocks?” by Carl M. Bender, Joshua Feinberg (arXiv:0709.2727 2007.09.17; J.Phys.A41:244004,2008) – http://arxiv.org/abs/0709.2727
- Abstract:

*The Riemann equation , which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This equation is symmetric. A one-parameter -invariant complex deformation of this equation, ( real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless is an odd integer.* - “No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model” by Carl M. Bender, Philip D. Mannheim (arXiv:0706.0207 2007.06.01; Phys.Rev.Lett.100:110402,2008) – http://arxiv.org/abs/0706.0207
- Abstract:

*Contrary to common belief, it is shown that theories whose field equations are higher than second order in derivatives need not be stricken with ghosts. In particular, the prototypical fourth-order derivative Pais-Uhlenbeck oscillator model is shown to be free of states of negative energy or negative norm. When correctly formulated (as a symmetric theory), the theory determines its own Hilbert space and associated positive-definite inner product. In this Hilbert space the model is found to be a fully acceptable quantum-mechanical theory that exhibits unitary time evolution.* - “Faster than Hermitian Quantum Mechanics” by Carl M. Bender, Dorje C. Brody, Hugh F. Jones, Bernhard K. Meister (arXiv:quant-ph/0609032 2006.09.05; Phys.Rev.Lett.98:040403,2007) – http://arxiv.org/abs/quant-ph/0609032
- Abstract:

*Given an initial quantum state |psi_I> and a final quantum state |psi_F> in a Hilbert space, there exist Hamiltonians H under which |psi_I> evolves into |psi_F>. Consider the following quantum brachistochrone problem: Subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time tau? For Hermitian Hamiltonians tau has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, tau can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from |psi_I> to |psi_F> can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing.* - “Equivalence of a Complex -Symmetric Quartic Hamiltonian and a Hermitian Quartic Hamiltonian with an Anomaly” by Carl M. Bender, Dorje C. Brody, Jun-Hua Chen, Hugh F. Jones, Kimball A. Milton, Michael C. Ogilvie (arXiv:hep-th/0605066 2006.05.08; Phys.Rev.D74:025016,2006) – http://arxiv.org/abs/hep-th/0605066
- Abstract:

*In a recent paper Jones and Mateo used operator techniques to show that the non-Hermitian -symmetric wrong-sign quartic Hamiltonian has the same spectrum as the conventional Hermitian Hamiltonian . Here, this equivalence is demonstrated very simply by means of differential-equation techniques and, more importantly, by means of functional-integration techniques. It is shown that the linear term in the Hermitian Hamiltonian is anomalous; that is, this linear term has no classical analog. The anomaly arises because of the broken parity symmetry of the original non-Hermitian -symmetric Hamiltonian. This anomaly in the Hermitian form of a -symmetric quartic Hamiltonian is unchanged if a harmonic term is introduced into . When there is a harmonic term, an immediate physical consequence of the anomaly is the appearance of bound states; if there were no anomaly term, there would be no bound states. Possible extensions of this work to quantum field theory in higher-dimensional space-time are discussed.* - “Calculation of the Hidden Symmetry Operator for a -Symmetric Square Well” by Carl M. Bender, Barnabas Tan (arXiv:quant-ph/0601123 2006.01.18; J.Phys.A39:1945-1953,2006) – http://arxiv.org/abs/quant-ph/0601123
- Abstract:

*It has been shown that a Hamiltonian with an unbroken symmetry also possesses a hidden symmetry that is represented by the linear operator . This symmetry operator guarantees that the Hamiltonian acts on a Hilbert space with an inner product that is both positive definite and conserved in time, thereby ensuring that the Hamiltonian can be used to define a unitary theory of quantum mechanics. In this paper it is shown how to construct the operator for the -symmetric square well using perturbative techniques.* - “PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics” by Carl M. Bender, Jun-Hua Chen, Kimball A. Milton (arXiv:hep-th/0511229 2005.11.23; J.Phys.A39:1657-1668,2006) – http://arxiv.org/abs/hep-th/0511229
- Abstract:

*A non-Hermitian Hamiltonian that has an unbroken PT symmetry can be converted by means of a similarity transformation to a physically equivalent Hermitian Hamiltonian. This raises the following question: In which form of the quantum theory, the non-Hermitian or the Hermitian one, is it easier to perform calculations? This paper compares both forms of a non-Hermitian quantum-mechanical Hamiltonian and demonstrates that it is much harder to perform calculations in the Hermitian theory because the perturbation series for the Hermitian Hamiltonian is constructed from divergent Feynman graphs. For the Hermitian version of the theory, dimensional continuation is used to regulate the divergent graphs that contribute to the ground-state energy and the one-point Green’s function. The results that are obtained are identical to those found much more simply and without divergences in the non-Hermitian PT-symmetric Hamiltonian. The $\mathcal{O}(g^4)$ contribution to the ground-state energy of the Hermitian version of the theory involves graphs with overlapping divergences, and these graphs are extremely difficult to regulate. In contrast, the graphs for the non-Hermitian version of the theory are finite to all orders and they are very easy to evaluate.* - “Semiclassical analysis of a complex quartic Hamiltonian” by Carl M. Bender, Dorje C. Brody, Hugh F. Jones (arXiv:quant-ph/0509034 2009.09.05; Phys.Rev.D73:025002,2006) – http://arxiv.org/abs/quant-ph/0509034
- Abstract:

*It is necessary to calculate the C operator for the non-Hermitian PT-symmetric Hamiltonian in order to demonstrate that H defines a consistent unitary theory of quantum mechanics. However, the C operator cannot be obtained by using perturbative methods. Including a small imaginary cubic term gives the Hamiltonian , whose operator can be obtained perturbatively. In the semiclassical limit all terms in the perturbation series can be calculated in closed form and the perturbation series can be summed exactly. The result is a closed-form expression for having a nontrivial dependence on the dynamical variables and and on the parameter .* - “Reflectionless Potentials and PT Symmetry” by Zafar Ahmed, Carl M. Bender, M. V. Berry (arXiv:quant-ph/0508117 2005.08.16; J.Phys.A38:L627-L630,2005) – http://arxiv.org/abs/quant-ph/0508117
- Abstract:

*Large families of Hamiltonians that are non-Hermitian in the conventional sense have been found to have all eigenvalues real, a fact attributed to an unbroken PT symmetry. The corresponding quantum theories possess an unconventional scalar product. The eigenvalues are determined by differential equations with boundary conditions imposed in wedges in the complex plane. For a special class of such systems, it is possible to impose the PT-symmetric boundary conditions on the real axis, which lies on the edges of the wedges. The PT-symmetric spectrum can then be obtained by imposing the more transparent requirement that the potential be reflectionless.* - “Dual PT-Symmetric Quantum Field Theories” by Carl M. Bender, H. F. Jones, R. J. Rivers (arXiv:hep-th/0508105 2005.08.15; Phys.Lett. B625 (2005) 333-340) – http://arxiv.org/abs/hep-th/0508105
- Abstract:

*Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a mass term the Hamiltonian is -symmetric. Depending on the mass parameter this symmetry may be either broken or unbroken. When the symmetry is unbroken, the spectrum of the quantum field theory is real. For the -symmetric version of the massive Thirring model in two-dimensional space-time, which is dual to the -symmetric scalar Sine-Gordon model, an exact construction of the operator is given. It is shown that the -symmetric massive Thirring and Sine-Gordon models are equivalent to the conventional Hermitian massive Thirring and Sine-Gordon models with appropriately shifted masses.* - “New Quasi-Exactly Solvable Sextic Polynomial Potentials” by Carl M. Bender, Maria Monou (arXiv:quant-ph/0501053 2005.01.11) – http://arxiv.org/abs/quant-ph/0501053
- Abstract:

*A Hamiltonian is said to be quasi-exactly solvable (QES) if some of the energy levels and the corresponding eigenfunctions can be calculated exactly and in closed form. An entirely new class of QES Hamiltonians having sextic polynomial potentials is constructed. These new Hamiltonians are different from the sextic QES Hamiltonians in the literature because their eigenfunctions obey PT-symmetric rather than Hermitian boundary conditions. These new Hamiltonians present a novel problem that is not encountered when the Hamiltonian is Hermitian: It is necessary to distinguish between the parametric region of unbroken PT symmetry, in which all of the eigenvalues are real, and the region of broken PT symmetry, in which some of the eigenvalues are complex. The precise location of the boundary between these two regions is determined numerically using extrapolation techniques and analytically using WKB analysis.* - “Introduction to PT-Symmetric Quantum Theory” by Carl M. Bender (arXiv:quant-ph/0501052 2005.01.11; Contemp.Phys.46:277-292,2005) – http://arxiv.org/abs/quant-ph/0501052
- Abstract:

*In most introductory courses on quantum mechanics one is taught that the Hamiltonian operator must be Hermitian in order that the energy levels be real and that the theory be unitary (probability conserving). To express the Hermiticity of a Hamiltonian, one writes , where the symbol denotes the usual Dirac Hermitian conjugation; that is, transpose and complex conjugate. In the past few years it has been recognized that the requirement of Hermiticity, which is often stated as an axiom of quantum mechanics, may be replaced by the less mathematical and more physical requirement of space-time reflection symmetry (PT symmetry) without losing any of the essential physical features of quantum mechanics. Theories defined by non-Hermitian PT-symmetric Hamiltonians exhibit strange and unexpected properties at the classical as well as at the quantum level. This paper explains how the requirement of Hermiticity can be evaded and discusses the properties of some non-Hermitian PT-symmetric quantum theories.* - “The C Operator in PT-Symmetric Quantum Theories” by Carl M. Bender, Joachim Brod, Andre Refig, Moritz Reuter (arXiv:quant-ph/0402026 2004.02.03) – http://arxiv.org/abs/quant-ph/0402026
- Abstract:

*The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian because Hermiticity guarantees that the energy spectrum is real and that the time evolution is unitary (probability preserving). This paper investigates an alternative way to construct quantum theories in which the conventional requirement of Hermiticity (combined transpose and complex conjugate) is replaced by the more physically transparent condition of space-time reflection (PT) symmetry. It is shown that if the PT symmetry of a Hamiltonian H is not broken, then the spectrum of H is real. Examples of PT-symmetric non-Hermitian quantum-mechanical Hamiltonians are and . The crucial question is whether PT-symmetric Hamiltonians specify physically acceptable quantum theories in which the norms of states are positive and the time evolution is unitary. The answer is that a Hamiltonian that has an unbroken PT symmetry also possesses a physical symmetry represented by a linear operator called C. Using C it is shown how to construct an inner product whose associated norm is positive definite. The result is a new class of fully consistent complex quantum theories. Observables are defined, probabilities are positive, and the dynamics is governed by unitary time evolution. After a review of PT-symmetric quantum mechanics, new results are presented here in which the C operator is calculated perturbatively in quantum mechanical theories having several degrees of freedom.* - “Finite-Dimensional PT-Symmetric Hamiltonians” by Carl M. Bender, Peter N. Meisinger, Qinghai Wang (arXiv:quant-ph/0303174; 2003.03.29) – http://arxiv.org/abs/quant-ph/0303174
- Abstract:

*This paper investigates finite-dimensional representations of PT-symmetric Hamiltonians. In doing so, it clarifies some of the claims made in earlier papers on PT-symmetric quantum mechanics. In particular, it is shown here that there are two ways to extend real symmetric Hamiltonians into the complex domain: (i) The usual approach is to generalize such Hamiltonians to include complex Hermitian Hamiltonians. (ii) Alternatively, one can generalize real symmetric Hamiltonians to include complex PT-symmetric Hamiltonians. In the first approach the spectrum remains real, while in the second approach the spectrum remains real if the PT symmetry is not broken. Both generalizations give a consistent theory of quantum mechanics, but if D>2, a D-dimensional Hermitian matrix Hamiltonian has more arbitrary parameters than a D-dimensional PT-symmetric matrix Hamiltonian.* - “Quantised Three-Pillar Problem” by Carl M. Bender, Dorje C. Brody, Bernhard K. Meister (arXiv:quant-ph/0302097; 2003.02.12) – http://arxiv.org/abs/quant-ph/0302097
- Abstract:

*This paper examines the quantum mechanical system that arises when one quantises a classical mechanical configuration described by an underdetermined system of equations. Specifically, we consider the well-known problem in classical mechanics in which a beam is supported by three identical rigid pillars. For this problem it is not possible to calculate uniquely the forces supplied by each pillar. However, if the pillars are replaced by springs, then the forces are uniquely determined. The three-pillar problem and its associated indeterminacy is recovered in the limit as the spring constant tends to infinity. In this paper the spring version of the problem is quantised as a constrained dynamical system. It is then shown that as the spring constant becomes large, the quantum analog of the ambiguity reemerges as a kind of quantum anomaly.* - “Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics” by Carl M. Bender, Peter N. Meisinger, Qinghai Wang (arXiv:quant-ph/0211166; 2002.11.26) – http://arxiv.org/abs/quant-ph/0211166
- Abstract:

*In a recent paper it was shown that if a Hamiltonian H has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT. The inner product with respect to CPT is associated with a positive norm and the quantum theory built on the associated Hilbert space is unitary. In this paper it is shown how to construct the operator C for the non-Hermitian PT-symmetric Hamiltonian using perturbative techniques. It is also shown how to construct the operator C for using nonperturbative methods.* - “All Hermitian Hamiltonians Have Parity” by Carl M. Bender, Peter N. Meisinger, Qinghai Wang (arXiv:quant-ph/0211123; 2002.11.26) – http://arxiv.org/abs/quant-ph/0211123
- Abstract:

*It is shown that if a Hamiltonian $H$ is Hermitian, then there always exists an operator P having the following properties: (i) P is linear and Hermitian; (ii) P commutes with H; (iii) ; (iv) the nth eigenstate of H is also an eigenstate of P with eigenvalue . Given these properties, it is appropriate to refer to P as the parity operator and to say that H has parity symmetry, even though P may not refer to spatial reflection. Thus, if the Hamiltonian has the form , where is real (so that H possesses time-reversal symmetry), then it immediately follows that H has PT symmetry. This shows that PT symmetry is a generalization of Hermiticity: All Hermitian Hamiltonians of the form have PT symmetry, but not all PT-symmetric Hamiltonians of this form are Hermitian.* - “Complex Extension of Quantum Mechanics” by Carl M. Bender, Dorje C. Brody, Hugh F. Jones (arXiv:quant-ph/0208076 2002.10.30; EconfC0306234:617-628,2003; Phys.Rev.Lett.89:270401,2002;) – http://arxiv.org/abs/quant-ph/0208076
- Abstract:

*It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but satisfies the less restrictive and more physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new Hamiltonians that one can construct to explain experimental data. One might expect that a quantum theory based on a non-Hermitian Hamiltonian would violate unitarity. However, if PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed physical symmetry C of the Hamiltonian. Using C, an inner product is constructed whose associated norm is positive definite. This construction is completely general and works for any PT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is governed by unitary time evolution. This work is not in conflict with conventional quantum mechanics but is rather a complex generalisation of it.* - “Quantum Complex Henon-Heiles Potentials” by Carl M. Bender, Gerald V. Dunne, Peter N. Meisinger, Mehmet Simsek (arXiv:quant-ph/0101095 2001.01.18; Phys.Lett. A281 (2001) 311-316) – http://arxiv.org/abs/quant-ph/0101095
- Abstract:

*Quantum-mechanical PT-symmetric theories associated with complex cubic potentials such as and , where is a real parameter, are investigated. These theories appear to possess real, positive spectra. Low-lying energy levels are calculated to very high order in perturbation theory. The large-order behavior of the perturbation coefficients is determined using multidimensional WKB tunneling techniques. This approach is also applied to the complex Henon-Heiles potential .* - “Variational Ansatz for PT-Symmetric Quantum Mechanics” by Carl Bender, Fred Cooper, Peter Meisinger, Van M. Savage (arXiv:quant-ph/9907008 ; Phys.Lett. A259 (1999) 224-231) – http://arxiv.org/abs/quant-ph/9907008
- Abstract:

*A variational calculation of the energy levels of a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian with N positive and x complex is presented. Excellent agreement is obtained for the ground state and low lying excited state energy levels and wave functions. We use an energy functional with a three parameter class of PT-symmetric trial wave functions in obtaining our results.* - “Complex Square Well — A New Exactly Solvable Quantum Mechanical Model” by Carl M. Bender (Washington U.), Stefan Boettcher (Emory U.), H. F. Jones (Imperial C.), Van M. Savage (Washington U.) (arXiv:quant-ph/9906057; J.Phys.A32:6771-6781,1999) – http://arxiv.org/abs/quant-ph/9906057
- Abstract:

*Recently, a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian was studied. It was found that the energy levels for this theory are real for all . Here, the limit as is examined. It is shown that in this limit, the theory becomes exactly solvable. A generalization of this Hamiltonian, () is also studied, and this PT-symmetric Hamiltonian becomes exactly solvable in the large- limit as well. In effect, what is obtained in each case is a complex analog of the Hamiltonian for the square well potential. Expansions about the large- limit are obtained.* - “Large-order Perturbation Theory for a Non-Hermitian PT-symmetric Hamiltonian” by Carl M. Bender, Gerald V. Dunne (arXiv:quant-ph/9812039; J.Math.Phys. 40 (1999) 4616-4621) – http://arxiv.org/abs/quant-ph/9812039
- Abstract:

*A precise calculation of the ground-state energy of the complex PT-symmetric Hamiltonian , is performed using high-order Rayleigh-Schr\”odinger perturbation theory. The energy spectrum of this Hamiltonian has recently been shown to be real using numerical methods. The Rayleigh-Schr\”odinger perturbation series is Borel summable, and Pad\’e summation provides excellent agreement with the real energy spectrum. Pad\’e analysis provides strong numerical evidence that the once-subtracted ground-state energy considered as a function of is a Stieltjes function. The analyticity properties of this Stieltjes function lead to a dispersion relation that can be used to compute the imaginary part of the energy for the related real but unstable Hamiltonian .* - “PT-Symmetric Quantum Mechanics” by Carl Bender (Washington U.), Stefan Boettcher (Los Alamos and Clark Atlanta U.), Peter Meisinger (Washington U.) (arXiv:quant-ph/9809072; J.Math.Phys. 40 (1999) 2201-2229) – http://arxiv.org/abs/quant-ph/9809072
- Abstract:

*This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition on the Hamiltonian, where represents the mathematical operation of complex conjugation and matrix transposition. This conventional Hermiticity condition is sufficient to ensure that the Hamiltonian $H$ has a real spectrum. However, replacing this mathematical condition by the weaker and more physical requirement , where represents combined parity reflection and time reversal , one obtains new classes of complex Hamiltonians whose spectra are still real and positive. This generalization of Hermiticity is investigated using a complex deformation of the harmonic oscillator Hamiltonian, where is a real parameter. The system exhibits two phases: When , the energy spectrum of is real and positive as a consequence of symmetry. However, when ; each of these complex Hamiltonians exhibits a phase transition at . These -symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space.* - “Quasi-exactly solvable quartic potential” by Carl M. Bender, Stefan Boettcher (CNLS, Los Alamos and CTSPS, Clark Atlanta University) (arXiv:physics/9801007; J.Phys. A31 (1998) L273-L277) – http://arxiv.org/abs/physics/9801007
- Abstract:

*A new two-parameter family of quasi-exactly solvable quartic polynomial potentials is introduced. Until now, it was believed that the lowest-degree one-dimensional quasi-exactly solvable polynomial potential is sextic. This belief is based on the assumption that the Hamiltonian must be Hermitian. However, it has recently been discovered that there are huge classes of non-Hermitian, -symmetric Hamiltonians whose spectra are real, discrete, and bounded below [physics/9712001]. Replacing Hermiticity by the weaker condition of symmetry allows for new kinds of quasi-exactly solvable theories. The spectra of this family of quartic potentials discussed here are also real, discrete, and bounded below, and the quasi-exact portion of the spectra consists of the lowest eigenvalues. These eigenvalues are the roots of a th-degree polynomial.* - “Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry” by Carl M. Bender, Stefan Boettcher (CNLS, Los Alamos, and CTSPS, Clark Atlanta University) (arXiv:physics/9712001; Phys.Rev.Lett. 80 (1998) 5243-5246) – http://arxiv.org/abs/physics/9712001
- Abstract:

*The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space. This paper describes the unusual classical and quantum properties of these theories.*

- “Response to Shalaby’s Comment on “Families of Particles with Different Masses in PT-Symmetric Quantum Field Theory”” by Carl M. Bender, S. P. Klevansky (arXiv:1103.0338; 2011.03.02) – http://arxiv.org/abs/1103.0338

## 2011.04.15

### Interesting visual arts sites

## Photography

Andrew Brooks:

- Andrew Brooks gallery online – http://www.andrewbrooksphotography.com/
- “Photoshopping Hundreds of Images Together to Recreate Our World” by Nicholas Jackson (The Atlantic; 2011.04.14) – http://www.theatlantic.com/technology/archive/2011/04/photoshopping-hundreds-of-images-together-to-recreate-our-world/237314/

Alexa Meade:

- “Still Life Still Alive” (Two Four Flinching Culture Hustler; 2010.11.01) – http://24flinching.com/word/gold-seal/inspiring-artists/still-life-still-alive/
- Alexa Meade home – http://www.alexameade.com/index.html

More:

- Peter Kemp photography: http://www.peterkemp.nl/
- Daria Andersen: http://dariaendresen.com/

## Magic Realism

- A Short History of Magic Realism – http://www.tendreams.org/magic-art.htm
- American Magic Realism gallery – http://www.tendreams.org/ammagic.htm
- European Magic Realism gallery – http://www.tendreams.org/euromagic.htm

Robert Vickrey

- “Robert Vickrey, Magic-Realist Painter, Dies at 84” by William Grimes (NYTimes; 2011.04.20) – http://www.nytimes.com/2011/04/20/arts/design/robert-vickrey-painter-of-magic-realism-school-dies-at-84.html
- Robert Vickrey (HARMON-MEEK GALLERY) – http://www.harmonmeek.com/artists/vickrey.html
- Egg Tempera – http://www.eggtempera.com/

- http://kuksi.com/
- Kris Kuksi: Divination and Delusion – http://thisartisyours.com/archive/2011/10/18/kris-kuksi-divination-and-delusion.html
*“A post-industrial Rococo master, Kris Kuksi obsessively arranges characters and architecture in asymmetric compositions with an exquisite sense of drama. Instead of stones and shells he uses screaming plastic soldiers, miniature engine blocks, towering spires and assorted debris to form his landscapes. The political, spiritual and material conflict within these shrines is enacted under the calm gaze of remote deities and august statuary. Kuksi manages to evoke, at once, a sanctum and a mausoleum for our suffocated spirit.”*

More of the kind here: Community and environmental art – https://eikonal.wordpress.com/2010/03/16/community-and-environmental-art/

## 2011.04.12

### Fermi paradox

- Fermi paradox (WikiPedia) – http://en.wikipedia.org/wiki/Fermi_paradox

## Be quiet you stupid young species! (or else be gone)

- “Is ET avoiding us out of a fear of human galactic conquest?” (io9; 2011.04.10) – http://io9.com/#!5790567/is-et-avoiding-us-out-of-a-fear-of-human-galactic-conquest
- “Is ET Scared of Human Conquest?” (13point7 blog) – http://thirteenpointseven.wordpress.com/2011/04/11/is-et-scared-of-human-conquest/
- “Interstellar Predation Could Explain Fermi Paradox” (The Physics arXiv blog; 2011.04.08) – http://www.technologyreview.com/blog/arxiv/26622/
*In a casual chat over lunch back in 1950, the Italian-American physicist Enrico Fermi posed a now famous question. If intelligent life has evolved many times in our galaxy and beyond, why do we see no sign of it?*

…

*Kent puts it like this: “If cosmic habitats are widely enough separated that they are very hard to ﬁnd, by far the best strategy for a typical species to avoid defeat in such competitions may be to avoid entering them, by being inconspicuous enough that no potential adversary identiﬁes its habitat as valuable.”**That raises important questions about whether humanity is wise to advertise its existence. Various attempts to send messages to the stars have already been made and many scientists have pointed out that this could be a serious mistake, even a suicidal one.* - “Too Damned Quiet?” by Adrian Kent (arXiv.org > physics > arXiv:1104.0624; 2011.04.04) – http://arxiv.org/abs/1104.0624
- Abstract:

*It is often suggested that extraterrestial life sufficiently advanced to be capable of interstellar travel or communication must be rare, since otherwise we would have seen evidence of it by now. This in turn is sometimes taken as indirect evidence for the improbability of life evolving at all in our universe. A couple of other possibilities seem worth considering. One is that life capable of evidencing itself on interstellar scales has evolved in many places but that evolutionary selection, acting on a cosmic scale, tends to extinguish species which conspicuously advertise themselves and their habitats. The other is that — whatever the true situation — intelligent species might reasonably worry about the possible dangers of self-advertisement and hence incline towards discretion. These possibilities are discussed here, and some counter-arguments and complicating factors are also considered.*

### Multitasking

- “Study: Older people worse at multitasking” bu Elizabeth Weise (ScienceFair; 2011.04.12) – http://content.usatoday.com/communities/sciencefair/post/2011/04/study-older-people-worse-at-multitasking/1
- “Older brains less nimble at multi-tasking – study” by Steve Gorman (Reuters; 2011.04.12) – http://www.reuters.com/article/2011/04/12/uk-science-elderly-idUSLNE73B03N20110412
- “Brain finds it difficult to multitask as we get older” (Daily News and Analysis; 2011.04.12) – http://www.dnaindia.com/lifestyle/report_brain-finds-it-difficult-to-multitask-as-we-get-older_1531188

### Inside black holes

- “Planets Could Orbit Singularities Inside Black Holes” (The Physics arXiv Blog; 2011.04.11) – http://www.technologyreview.com/blog/arxiv/26626/
*The discovery of stable orbits inside certain kinds of black hole implies that planets and perhaps even life could survive inside these weird objects, says one cosmologist* - “Is there life inside black holes?” by Vyacheslav I. Dokuchaev (arXiv.org > gr-qc > arXiv:1103.6140; 2011.04.09) – http://arxiv.org/abs/1103.6140
- Abstract:

*Inside the rotating or charged black holes there are bound periodic planetary orbits, which not coming out nor terminated at the central singularity. The stable periodic orbits inside black holes exist even for photons. We call these bound orbits by the orbits of the third kind, following to Chandrasekhar classification for particle orbits in the black hole gravitational field. It is shown that an existence domain for the third kind orbits is a rather spacious, and so there is a place for life inside the supermassive black holes in the galactic nuclei. The advanced civilizations of the third kind (according to Kardashev classification) may inhabit the interiors of supermassive black holes, being invisible from the outside and basking as in the light of the central singularity and the orbital photons.*

Related here: Astronomy & Astrophysics – https://eikonal.wordpress.com/2011/05/09/astronomy-astrophysics/ | Astronomic tables and calculators – https://eikonal.wordpress.com/2010/01/28/astronomic-tables-and-calculators/ | Solar planetary system – https://eikonal.wordpress.com/2011/02/17/solar-planetary-system/ | Physics Sites – https://eikonal.wordpress.com/2010/02/12/physics-sites/

## 2011.04.08

### Anti-scientism

- “Science Is Not Your Enemy – An impassioned plea to neglected novelists, embattled professors, and tenure-less historians” by Steven Pinker (New Republic; 2013.08.06) – http://www.newrepublic.com/article/114127/science-not-enemy-humanities
- “No, Science Doesn’t Have All the Answers” by New Republic Literary Editor Leon Wieseltier (New Republic; 2013.08.07) – http://www.newrepublic.com/article/114172/leon-wieseltier-scientism-and-humanities | = Leon Wieseltier on the Value of the Humanities – http://www.youtube.com/watch?v=GevfKLmmMr0#at=110
- “The Trouble with Scientism – Why history and the humanities are also a form of knowledge” by Philip Kitcher – http://www.newrepublic.com/article/books-and-arts/magazine/103086/scientism-humanities-knowledge-theory-everything-arts-science
- “Science’s Sacred Cows (Part 1)” by Dave Pruett (Huffington Post; 2013.01.02) – http://www.huffingtonpost.com/dave-pruett/sciences-sacred-cows-part-1_b_2392381.html?
- “Time to Separate Scientism and State” by Wesley J. Smith (2012.12.24; national Review online) – http://www.nationalreview.com/human-exceptionalism/336436/time-separate-scientism-and-state
- “Politicians must not elevate mere opinion over science” by Brian Cox and Robin Ince (NewStatesman; 2012.12.18) – http://www.newstatesman.com/sci-tech/sci-tech/2012/12/brian-cox-and-robin-ince-politicians-must-not-elevate-mere-opinion-over-sc

- “The Folly of Scientism” by Austin L. Hughes (The New Atlantis; 2012 Fall) – http://www.thenewatlantis.com/publications/the-folly-of-scientism
- “Philosophy Is Not a Science” by Julian Friedland (The new York Times; 2012.04.05) – http://opinionator.blogs.nytimes.com/2012/04/05/philosophy-is-not-a-science/
- “The New Intolerance” by melanie Phillips (Standpoint; 2012.05) – http://standpointmag.co.uk/text-may-12-the-new-intolerance-melanie-phillips-secularism-religion-intolerance-atheism-islamism-scientism
- “Defending Freedom” by george Lakoff (New Repoblic; 2006.10.16) – http://www.newrepublic.com/article/politics/defending-freedom
- “Block That Metaphor” by Steve npinker [- a review of “Whose Freedom?: The Battle over America’s Most Important Idea” by George Lakoff (The New Republic; 2006.10.19)] – http://www.powells.com/review/2006_10_19
- “Frame Game” by The New Republic staff (The New Republic; 2006.11.04) – http://www.newrepublic.com/blog/open-university/frame-game

## USA:Anti-Evolution

- “Tennessee Bill Helps Teachers Challenge Evolution” (SlashDot; 2011.04.08) – http://science.slashdot.org/story/11/04/08/1353249/Tennessee-Bill-Helps-Teachers-Challenge-Evolution
*“In a 70-28 vote yesterday, the Tennessee House of Representatives passed HB 368 (PDF), a bill that encourages science teachers to explore controversial topics without fear of reprisal. Critics say the measure will enable K-12 teachers to present intelligent design and creationism as acceptable alternatives to evolution in the classroom. If the bill passes, Tennessee would join Louisiana as the second state to have specific ‘protection’ for the teaching of evolution in the classroom.”* - “Bill Allowing Teachers to Challenge Evolution Passes Tennessee House” by Sara Reardon 9Science; 2011.04.07) – http://news.sciencemag.org/scienceinsider/2011/04/bill-allowing-teachers-to-challenge.html

## USA: Anti – Climate Change

### Geolocation

- “SimpleGeo Makes Location Data Free, Complicates Smartphone Tracking Worries” by Kit Eaton (Fast Company; 2011.04.22) – http://www.fastcompany.com/1749262/simplegeo-makes-location-data-free-complicates-smartphone-tracking-worries
- “Involuntary Geolocation To Within One Kilometer” 9SlashDot; 2011.04.08) – http://yro.slashdot.org/story/11/04/08/1245244/Involuntary-Geolocation-To-Within-One-Kilometer
*Schneier’s blog tips an article about research into geolocation that can track down a computer’s location from its IP address to within 690 meters on average without voluntary disclosure from the target. Quoting: “The first stage measures the time it takes to send a data packet to the target and converts it into a distance – a common geolocation technique that narrows the target’s possible location to a radius of around 200 kilometers. Wang and colleagues then send data packets to the known Google Maps landmark servers in this large area to find which routers they pass through. When a landmark machine and the target computer have shared a router, the researchers can compare how long a packet takes to reach each machine from the router; converted into an estimate of distance, this time difference narrows the search down further. ‘We shrink the size of the area where the target potentially is,’ explains Wang. Finally, they repeat the landmark search at this more fine-grained level: comparing delay times once more, they establish which landmark server is closest to the target.”* - “Internet probe can track you down to within 690 metres” by Jacob Aron(NewScientist; 2011.04.05) – http://www.newscientist.com/article/dn20336-internet-probe-can-track-you-down-to-within-690-metres.html
*Online adverts could soon start stalking you. A new way of working out where you are by looking at your internet connection could pin down your current location to within a few hundred metres.* - “Pinpointing a Computer to Within 690 Meters” by Bruce Schneier (2011.04.08) – http://www.schneier.com/blog/archives/2011/04/pinpointing_a_c.html

Related here:

- iPhone (and Androids, too) doing surveilance, on whose behalf? – https://eikonal.wordpress.com/2011/04/21/iphone-doing-surveilance-on-whose-behalf/:
- packetlss – Android location service cache dumper – https://github.com/packetlss/android-locdump
- iPhone Tracker – http://petewarden.github.com/iPhoneTracker/

## 2011.04.04

### lastlog

- freq – lastlog analyzer – http://www.bangmoney.org/projects/freq/
- Formatting and Printing Lastlog – http://www.hcidata.info/lastlog.htm

### Unix pages (at this blog)

- Unix system administration – https://eikonal.wordpress.com/2011/03/02/unix-system-administration/
- Unix tricks – https://eikonal.wordpress.com/2011/02/15/unix-tricks/
- Unix hardening – https://eikonal.wordpress.com/2010/04/20/unix-hardening/
- Logging – https://eikonal.wordpress.com/2010/04/13/logging/
- PAM – https://eikonal.wordpress.com/2011/03/11/pam/
- SSH, OpenSSH – https://eikonal.wordpress.com/2010/12/16/ssh-openssh/
- Unix “script” command – https://eikonal.wordpress.com/2010/12/02/unix-script-command/
- vi editor – https://eikonal.wordpress.com/2010/11/15/vi-editor/
- sed tricks – https://eikonal.wordpress.com/2010/10/05/sed-tricks/
- Nmap options, switches and uses – https://eikonal.wordpress.com/2010/09/20/nmap-options-swtiches-and-uses/
- netcat – https://eikonal.wordpress.com/2010/07/12/netcat/
- Command line based text replace – https://eikonal.wordpress.com/2010/07/13/command-line-based-text-replace/
- Archiving and compression tools – https://eikonal.wordpress.com/2010/08/03/archiving-and-compression-tools/
- Cygwin – https://eikonal.wordpress.com/2010/07/12/cygwin-stuff/
- googlecl – https://eikonal.wordpress.com/2010/07/06/googlecl/
- John the Ripper – https://eikonal.wordpress.com/2010/05/25/john-the-ripper/