Philosophia Naturalis #8

This post was delayed by a number of ridiculous technical mishaps, but issue number eight of Philosophia Naturalis - the physics blogosphere’s very own blog carnival – is finally here. There were a number of very interesting submissions spanning pretty much everything that is involved in physics and the practice of it, and so I’ve split them up accordingly. Enjoy!

Cool Experiments
Motivated by some recent quantum optics work recording the birth and death of microwave photons in a superconducting resonant cavity by a French group, Chad Orzel has proclaimed this to be “the golden age of experimental quantum optics”. And indeed, it seems to be: two other such experiments include this study of the Hanbury-Brown-Twiss effect, and this more recent realization of the delayed-choice experiment first proposed by John Wheeler in 1978. A closely related experiment is that of the ‘quantum eraser’ proposed by Scully and Drühl in 1981, and this post does an excellent job of summarizing the general principles.

On the opposite end of the size spectrum, Cosmic Variance recently hosted a very interesting discussion on some analysis of cosmic microwave background radiation data from WMAP (NASA’s much-publicized effort to very accurately measure the temperature of the CMB).

Interesting Theory
As tends to be the case, most posts were of a more theoretical bent. The mapping of the E₈ Lie group recently received a good deal of press, including a rather vague article in the New York Times (the gist of which was something along the lines of “a bunch of mathematicians did something really complicated involving a pretty picture, and apparently it has profound implications but we’re not exactly sure what.”) Mark Chu-Carroll and John Baez have taken a different approach, recently posting about the actual math involved and the whole point of the project. And speaking of recent math-y work that has received a good deal of press, these two posts report on this paper by Peter Lu and Paul Steinhardt (who used to be at Penn!) on signatures of quasicrystalline Penrose tilings in medieval Islamic architecture.

Penrose is an excellent segway into two posts by Scott Aaronson. The first poses the question: “what’s the connection between a black hole having an event horizon and its having a singularity? In other words, once you’ve clumped enough stuff together that light can’t escape, why have you also clumped enough together to create a singularity?” (This is related to the Penrose-Hawking theorems of general relativity). The second (or rather, the subsequent comments) deals with possible connections between the brain and quantum computers, something Roger Penrose has discussed in a good deal of depth. (Matt Leifer has a similar post, asking the question: “if quantum computers are more efficient than classical ones then why didn’t our brains evolve to take advantage of quantum information processing?“)

There’s more out there, too: see, for example, this post discussing the much-storied Bayesian theorem and connections to Bell’s inequalities, or this post on ‘biophysical economics’, an economic theory rooted in biological and physical realities first put forth in the 20’s. Something that struck me as being particularly interesting was this post on the use of evolutionary algorithms in lattice QCD simulations. Meanwhile, Ponder Stibbons has been plowing through Huw Price’s book (Time’s Arrow and Archimedes’ Point) on some of the more philosophical questions of physics, with posts on Price’s objection to dynamical explanations of entropy increase (“they can never account for the asymmetry in our observations unless they themselves have asymmetric assumptions”) and a modern-day version of Olbers’ paradox.

And of course, a good deal of very interesting physics (albeit of a different sort) goes into fields of inquiry that some would consider unconventional, like geophysics. These two posts dealing with earthquakes and volcanoes touch on this to a certain extent. The latter is particularly interesting, looking into the various possible triggers for volcanoes (and drawing connections between large earthquakes and volcanic eruptions, motivated by a fictional account of Charles Darwin’s journey on The Beagle).

The Culture of Physics
Speaking of geophysics, Jennifer Oullette has written about a talk at the recent APS March Meeting on large-scale pattern formation in geological systems, citing some work by Meredith Betterton (who gave a talk here at Penn on an unrelated subject recently) on the creation of artificial spiky ice formations. (March Meeting is an event when thousands of physicists get together and tell each other about what they’re working on – held, incidentally enough, in March.) A number of people have posted about various events at March Meeting; see, for example, this other post by Jennifer Oullette, this post by Travis Hime, and this one by Doug Natelson – or see the PhysicsWeb blog.

Having huge meetings and partying like rock stars isn’t everything, though. Among other things, the physics community (just like any other) has its share of scandals, politics, marketplace tactics, things of that sort. Sabine Hossenfelder, for example, has recently blogged about the problems of treating the scientific community as a marketplace, while Julianne Dalcanton’s post on physics’ “cult of genius” definitely touched a nerve among readers. Meanwhile, Clifford Johnson has shared his views on recent events regarding an imprisoned theoretical physics grad student. (And of course, there’s the media aspect of things: John Conway recently picked up on his two previous posts on the search for the Higgs boson to blog about the unexpected media response.)

Communicating Physics
Tommaso Dorigo recently posted about some of the problems associated with the way physicists communicate things to laypeople, dealing specifically with an example from high energy physics (what is a lower limit at 95% confidence level, anyway?). At the end of the day, the physics blogosphere’s rather good with this kind of thing. For example, ‘basic concepts’ posts (like the ones mentioned in this excellent post, or this one – part of a series – on special relativity) do an excellent job. And hey, communicating physics is kind of the whole point of this blog carnival, in a sense. I think that’s where I’ll end things – hopefully it’s been interesting. Thanks to everyone who submitted either their posts or someone else’s.

High-Energy Materials Science

Someone I know recently asked me about this recent New Scientist article, and honestly, I’m not sure what to make of it. To summarize the article, ‘string-net condensation‘ (a model in which “electrons are not really elementary, but are formed at the ends of long ’strings’ of other, fundamental particles”) predicts interesting new phases of matter in certain spin models, and recent experiments on the amusingly-named Herbertsmithite may be a signature of one such phase of matter.

The subject matter is definitely interesting, although I am in no position to comment on the actual science (especially the theory, because I don’t understand it – my very little exposure to renormalization group theory so far has been in the context of statistical mechanics). On the experimental side, there is no doubt that recent work studying material properties of this system (such as looking at the specific heat or the temperature-dependence of the magnetic susceptibility, as well as using inelastic neutron scattering) is yielding some very cool physics. And of course on the theory side of things, it is clear that being able to come up with a unified theory from which electrons and photons are emergent is a Big Deal. The problem I have is that while the New Scientist article makes it sound like these measurements are a clear signature of a new phase of matter as predicted by string-net condensation, I can’t really discern the degree to which the link between the theory and experiments is scientifically rigorous, at least from reading the relevant papers. Rather, the article strikes me as being yet another example of really bad sensationalist journalism (see this post by Doug Natelson for more).

However, I find this to be a nice example of how things like high-energy physics theories of string-net condensation or quantum electrodynamics are becoming increasingly important in the study of materials. The ‘hot’ material for this kind of thing these days is obviously graphene, the “new bridge between condensed matter physics and quantum electrodynamics“. Another surprising example of this, for example, is this recent paper connecting SU(2) Yang-Mills theory in the low-temperature phase to nematic liquid crystals (who’d have thought? Certainly not me – I found it amusing that the only equations in the paper I actually understood were 18-20, the ones relating to liquid crystals).

And of course, this Herbertsmithite stuff is an example of another big thing in condensed matter physics – namely, ‘discovering’ new states of matter (at least theoretically). A lot of interesting physics is coming out of this effort, such as this recent work by Shoucheng Zhang at Stanford.

Quantum Information, et cetera

Today’s been a pretty exciting day. Among other things, we finally used all these abstract concepts relating to modules that we’ve been developing in my algebra class to derive some really neat results: in particular, rational canonical form and Jordan canonical form for matrices that can’t be diagonalized. There’s just something about taking all this seemingly useless theory and deriving something nice (and not so obvious) that you can actually use from it that’s very satisfying. Hey, I may even blog about it at some point. Another interesting math idea today was the subject of a colloquium that I wasn’t able to attend (but found out a good deal about from those who did): can we hear the shape of a drum? (Among other things, the question ties in with work done by our Dean, NASA’s WMAP project/this PRL, and the general notion of inverse problems such as those people deal with in things like MRI). And of course, my abstract algebra recitation session turned into me arguing with my TA (an algebraic geometer) and a computer scientist about why statistical mechanics is The Coolest Thing ever. What can I say? Never get me started on statistical mechanics – it’s just such a gorgeous subject, and I can’t get enough of it.

Anyway, while the math colloquium was going on, I was off at today’s physics colloquium by Prof. Charles Marcus of Harvard University, something I’ve been looking forward to for a good deal of time now. And what a talk it was: although I would have preferred more technical details, the talk catered to a pretty general audience, and it was perhaps the clearest physics talk I’ve been to in a long time. He started off by reviewing the history of computation (from the Antikythera mechanism of 150 BC to the first integrated circuit, 50-ish years ago), noting that quantum information processing is really a new paradigm in this history (to paraphrase, the parallelism in computation implied by the multiplicity of states inherent in quantum mechanics is something that hasn’t really been possible till now) and surveying recent developments in solid-state implementations of controllable qubits from his lab. Most of the relevant papers are on his lab webpage (linked above), and a lot of the technical details are presented in this talk he gave at KITP in 2006, although he did present some very recent data pertaining to this paper. All in all, a very cool talk – I especially like the terminology in this field, what with the ‘Zamboni’ effect and ‘bucket brigades’.

I can’t wait for next month’s colloquium – David Nelson will be speaking!

Tonks-Girardeau Gas

I had the chance to kick back and read a few papers over spring break, including a number of experimental biophysics and atomic/molecule/optical (AMO) physics papers for well-roundedness. Some dealt with the Tonks-Girardeau gas, something I first encountered in my liquid crystals class last semester (I’m taking a few of the equations below from my notes from that class). Among other things, this system is interesting because it was one of the first exactly-solvable systems in statistical mechanics, of which there still remain very few (the Ising model in 1D/2D being another). From a soft condensed-matter physics point of view, the Tonks gas serves as a good starting point for exploring the notion of excluded volume, a surprisingly important concept (for example, leading to ideas like the depletion attraction and entropic attraction/organization – see this book for a nice introduction.)

Working at the research laboratory of the General Electric company, John Bradshaw Taylor and Irvin Langmuir spent a good deal of time in the early 30’s developing very precise means of determining the number of caesium atoms adsorbed on tungsten and using these to study the properties of such monoatomic films. Motivated by this, Lewi Tonks derived the equation of state not just for a two-dimensional gas, but for a one-dimensional and three-dimensional gas as well, ignoring the nature of the forces between them and treating the simplest case of hard elastic spheres. (Twenty-four years later, Marvin Girardeau established a rigorous one-to-one correspondence between this system and a 1D system of spinless fermions. This ‘fermionization’ helps explain why such a system of bosons doesn’t undergo condensation.)

For example, one can calculate the equation of state for a dilute gas of strongly-interacting impenetrable bosons confined to the one dimensional space quite simply – since we’re treating the particles as hard spheres of radius , the associated potential is given by for and for . Then the -sphere partition function is just:

(There’s a constant prefactor involving and what Kittel & Kroemer call the quantum concentration, but it’s not important here since we’ll be taking derivatives.) A slick way of solving this is by changing variables to :

and since and , where in this case the ‘volume’ , one finds that

It is interesting to note that including a simplistic two-body attractive interaction regains the van der Waals equation of state exactly (see for example section 4.9 of Mattis’ somewhat misleadingly-titled book on statistical mechanics). This can also be extended to three dimensions by expanding the expression for P and considering the virial expansion, and a lot of interesting concepts, like the depletion interaction, fall out very nicely (see the first chapter of the soft condensed-matter physics book I mentioned above).

Another soft-matter application of the Tonks gas that I came across a while back is this paper by Tom Chou at UCLA. He’s developed an exact one-dimensional theory of histone adsorption and wrapping on DNA by considering each histone as a Tonks gas particle, which I think is pretty neat; after all, histones are pretty much hard spheres confined to a line of sorts – as wikipedia puts it, they “act as spools around which DNA winds”.

(This model can be theoretically extended in other ways, too. For example, Takahashi added in the effect of an arbitrary bounded interaction potential between going from the zero potential to the infinite hard-core potential; see another book by Mattis for more on this.)

But the Tonks gas is important in other areas of physics, as well – in particular, in the study of atomic gases at low temperature and particle density. During the summer of 2004, two groups published papers detailing their experiments using ultracold rubidium-87 atoms trapped using optical lattices in which they observed a transition to the strongly-correlated 1D Tonks gas regime (although they verified this in different ways: the Penn State group studied the energy and size of their system while the European group looked at the momentum distribution, both comparing their results to relevant theoretical predictions). And the research has been continuing ever since: for example, the Penn State group has extended these measurements to the study of a quantum Newton’s cradle, and other groups have studied 1D Bose gases as both Mott insulators and Luttinger liquids (the latter being a particularly nice connection to carbon nanotubes).

Conan O’Brien/Jim Carrey

I just came across this video via a friend of mine. It is, quite simply, a work of genius.

Jim Carrey: I was just reading this incredible paper on the stochastic phase-shifting of the parametrically-driven electron in a Penning trap; and apparently, a bistability arises dynamically in the specific parametrically-driven systems, because the phase of the electron’s steady-state oscillation can either have the two values separated by .

(…)

Conan O’Brien: You know, it’s funny, what shocks me about an electron in a Penning trap is that most amplitude collapses are accompanied by a phase flip. Given that the rate of escape from the trap depends exponentially on an activation energy as the diffusion constant approaches and approaches .

JC: Absolutely. No question there.

Max Weinberg: I don’t know about that, Conan. Have you considered that the parametric driving force excites a nearly-resonant electron oscillation at the drive frequency, ? It’s a classic example of the period-doubling that occurs when a linear oscillator is strongly driven.

JC: Max. Did you just say that ?

MW: Yeah.

CB: (Laughs). It’s actually ! Wow, Max. Max, you know nothing about quantum physics!

MW: You’re right.

As far as I can tell, they’re alluding to this 1999 Gabrielse paper. Speaking of neat things that can be done with electrons and Penning traps, I recently came across these two other recent Gabrielse papers reporting very precise measurements of the electron magnetic moment and fine structure constant, which is pretty neat.

Anyway, back to work for me. Spring break is just a day away…