RIP Richard L. Liboff (1931–2014)

Steve Strogatz just e-mailed me to let me know that Richard Liboff, my PhD supervisor, has died. The obituary only came out yesterday, but Richard died on 9 March. The comment, which is recalled in the Cornell obituary, that Richard made about his book in the Spiderman movie was quintessentially him. (I remember that incident when Cornell first had a press release about it.)

Richard seemed pretty crazy at times (though, to be honest, I bet that my students would say the same thing about me!), and we ultimately had a falling out (and I couldn't get him to respond to e-mails after fall 2003 or early 2004), but I do have a soft spot for him --- and I have some of my own stories to tell, of course. Richard was quite a character, and Cornell's obituary conveys it very well. In some ways, this is like the closing of a final bit of my graduate-school chapter, although I still have strong contacts with many of the Cornell faculty.

Here is a link to Richard's wikipedia page. He is best known for his quantum mechanics book, of course. (Given how well-known his book is, I'm rather surprised that his obituary hasn't circulated much more widely. It certainly deserves to be. Through his textbooks, Richard made extremely important expository contributions to generations of young physicists and other scientists.)

I published my first science paper jointly with Richard. It is nowhere near my best paper, but it will always be my first one.

Update (5/25/14): I noticed that this blog entry was getting several hits, so I tried to figure out the mechanism via Google (no luck yet). In the process, though, I found something really interesting that I never knew: Richard self-published a novel! (Given the details of the Amazon page, I am assuming that it was self-published.)

RIP Martin Gutzwiller (1925–2014)

It went under my radar, but Martin Gutzwiller (a pioneer in quantum chaos and other fields of physics) died on 3 March 2014. I was looking him up because I am sitting in a small library (and, seemingly, game room) in MPIPKS and I noticed a collection that was donated by a former Martin Gutzwiller Fellow, which I didn't realize they had here. Here is Gutzwiller's MPIPKS page.

Quantum Chaos in Nature

Doug Stone has a News and Views article about quantum chaos in the June 10, 2010 issue of Nature.

In case you don't have full-article access to Nature, you can find the abstract here (it's the second article).

RIP George Zaslavsky (1935-2008)

In November, the field of quantum chaos lost another of its pioneers.

In this case, it was George Zaslavsky of NYU.

I haven't found an extensive obituary online, but here is a very brief biography.

Chaos's nonlinear science gallery on YouTube

Sometimes one can actually get somewhere with requests to journals.

I was reading an issue of SIAM News a few months back and notice that a video of Doug Arnold (from University of Minnesota) on Moebius transformations had achieved an astounding level of popularity on YouTube. (I had also heard at undergraduate research conferences about various math professors who used YouTube for teaching purposes.)

This is a great way to get more science out to the public, so I e-mailed David Campbell, Editor-in-Chief of the journal Chaos, which publishes the Nonlinear Science Gallery every year. This gallery includes video entries, which would be absolutely perfect for YouTube. I have also known David for a few years, and in fact am writing an expository article on the Fermi-Pasta-Ulam problem with him and a couple of other people, and I figured he would be receptive to the idea. The key hurdle would be the thoughts of the publisher (American Institute of Physics).

David got back to me while I was visiting Caltech last week to give me the news that AIP supported the endeavor, and now I'm writing this entry to announce that Chaos's YouTube page has gone live.

Among the videos is one that I coauthored with Caltech undergrad Tom Mainiero. It's currently the 2nd most watched video among the Chaos collection and perhaps with your help it can become #1. It even has a catchy tune in the background. (Though I am a bit perplexed that YouTube lists an Adolf Hitler speech as a related video.)

RIP Boris Chirikov (1928-2008)

Here's another death I missed, and in this particular case I am very surprised that it escaped my notice. On February 12th, Boris Chirikov, one of the founding fathers of both Hamiltonian chaos and quantum chaos, died. I got my Ph.D. thesis in quantum chaos, and of course this blog is named after that field. I continue to do research in both of these subjects, which are near and dear to my heart. Among Chirikov's contributions to these fields are his development of his eponymous Chirikov overlap criterion (which played an important role in the investigation of chaos in the Fermi-Pasta-Ulam problem and describes the transition from locally chaotic dynamics to globally chaotic dynamics) and equally eponymous Chirikov-Taylor map (aka, the "standard map").

Update: Here is a link to the obituary in the online version of Physics Today.

What is quantum chaos?

In January, the Notices of the American Mathematical Society published a short article in their 'What is...' series called What is... Quantum Chaos. It was written by Ze'ev Rudnick, and if you look very closely, you'll find that I am mentioned in the article. (Alex Barnett, another quantum chaotician from my generation, is also mentioned. Lots of old people are mentioned too.)

The article does a very nice job of describing the gist of quantum chaos, so I wanted to post a link to it here (given that this field forms the namesake for my blog, and also given that I wrote my dissertation on this topic). Here is the wikipedia page for quantum chaos. (By the way, if you google 'wikipedia quantum chaos', my research synopsis web page comes up third. This was a happy byproduct of linking to the page in order to help prospective students and postdocs know what the subject is in case they want to work with me on it.) A 1992 article that Martin Gutzwiller wrote in Scientific American after encouragement by Predrag Cvitanovic provides an excellent introduction to the subject for intelligent people who aren't physicists or mathematicians.

To explain very briefly, quantum systems can't actually exhibit a rigorous form of sensitive dependence on initial conditions (the butterfly effect; small differences in initial conditions leading to exponentially large divergence of trajectories) the way that classical systems can. (For one thing, there is the issue of defining something that corresponds to a trajectory in quantum mechanics, though the headaches don't end there.) However, if I hold a classical chaotic system in one hand (for simplicity, say that it's fully chaotic rather than mixed) and a classically non-chaotic (regular, integrable) system in the other and I quantize them both, I can tell which one was which based on certain properties (like the distributions of the spectra, the scarring of classical periodic orbits, and so on) of the quantum systems even though I can't define chaos rigorously in those systems. In the case of mixed systems with well-separated regular and chaotic regions, one can see the signatures of the different regions. (For example, see the paper that my student, Tom Mainiero, and I published in Chaos in December 2007. Also see recent work by Alex Barnett on quantum mushroom billiards.) If the different types of regions are not well-separated, then it can get pretty hard and lots of subtleties ensue. (Actually, lots of subtleties ensue even before you start dealing with the quantization of systems with poorly-separated mixtures of regular and chaotic regions. It's just that there are even less tractable subtleties that arise when the regions are completely interspersed with each other.)

This entry was longer than I intended, but I hope it can give normal people some idea of what quantum chaos is.

"Quantization of a free particle interacting linearly with a harmonic oscillator"

As just promised, the full-length article that I wrote with my former SURF student Tom Mainiero just came out. The proofing stage took a little longer than usual; in fact, the journal was apparently waiting on our final approval after several proof iterations (with a couple of mess-ups on our part and a rather large number of mess-ups on their part --- including forgetting to capitalize the title of the article, changing our grammatically-correct corrections to grammatically incorrect statements [which I found irksome], and a comedy of errors in the display style for one of the equations) in order to finish posting the final articles in their December 2007 issue. I definitely managed to annoy the publishers a bit for this particular article (they gave this away with a couple of statements in the notes they conveyed to us along with the second set of page proofs), but if they're not going to implement one of my corrections (or if they adjust how they do so), I expect an explanation of why or else I'm just going to ask them to correct it again when I get the subsequent round of page proofs. As anybody who knows me should know, I am extremely anal about things like this; just look at how I mark up the pages of any paper drafts that my students have submitted to me! Of course, the publishers and typesetters were very much attempting to get things right -- they were just a little sloppier than I would have liked on this particular occasion.

The article is titled, "Quantization of a free particle interacting linearly with a harmonic oscillator."

The abstract reads as follows:

We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the quantization of mixed systems. We identify key signatures of the classically chaotic and regular portions in the quantum system by constructing Husimi distributions and investigating avoided level crossings of eigenvalues as functions of the strength and range of the interaction between the system’s two components. We show, in particular, that the Husimi structure becomes mixed and delocalized as the classical dynamics becomes more chaotic.


I think the best thing to add to convey which this is interesting, let me also reproduce the bold introductory paragraph from the article:

Typical classical Hamiltonians systems are neither fully integrable nor fully chaotic, but instead possess mixed dynamics, with islands of stability situated in a chaotic sea. In this paper, we investigate the quantization of a recently-studied system with mixed dynamics [1]. This example consists of a free particle that moves around a ring that is divided into two regions. At the boundaries between these regions, the particle is kicked impulsively by a harmonic oscillator (in a manner that conserves the system’s total energy), but the particle and oscillator otherwise evolve freely. Although the system is not generic, its separation into regular and chaotic components also allows more precise investigations (both classically and quantum-mechanically) than is typically possible, making this an ideal example to achieve a better understanding of the quantization of mixed systems. By examining avoided level crossings and Husimi distributions in the quantum system, we investigate the quantum signatures of mixed dynamics, demonstrating that the Husimi structures of nearby states become mixed and delocalized as chaos becomes a more prominent feature in the classical phase space.

"Avoided Level Crossings in the Quantization of a Mixed Regular-Chaotic System"

In March 2007, my student Tom Mainiero and I submitted a "videos/mainieroporter_0011.wmv">video entry for the Nonlinear Science Gallery on display at the APS March Meeting. (Don't forget to crank up the volume to full blast before you click on the link to the video.)

Today, the one-page article based on this video was posted by Chaos. (The research article based on the same project will be appearing in Chaos in the very near future --- possibly within a few days.)

The one-page article basically functions as an extended abstract, so I won't comment on the project itself here. I'll discuss it a bit more when I post a blog entry about the research article.

Prime Numbers Get Hitched

Here is an interesting article about the role of 42 in strengthening links between quantum mechanics and number theory (which is very closely related to certain aspects of quantum chaos, by the way).

Additionally, in the condensed matter theory group meeting on 12/4, the speaker a certain type of dynamical behavior in his problem that occurred for "n less than equal to 41" (where n is an integer), which caused a few of us to go in a certain direction.

In continuing the discussion of numbers, this is post number 664.