Incredibly pointless paper

This has to be one of the most useless things I've ever seen on the arxiv. Basically, the authors point out that there is absolutely no chance of the helium coolant of the LHC magnet system suddenly deciding to explode. Gee, really?! It is just sad that someone felt compelled to write this.

This paper reminds me of the old Annals of Improbable Research article, "The Effect of Peanut Butter on the Rotation of the Earth".

A subtle statistical mechanics question

A faculty colleague of mine posed a statistical physics question for me, since I'm teaching that subject to undergraduates this semester, and I want to throw it out there to my readership. I'll give some context, explain the question, and then explain why it's actually rather subtle. If someone has a good answer or a reference to a good (that is, rigorous) answer, I'd appreciate it.

In statistical physics one of the key underlying ideas is the following: For every macroscopic state (e.g., a pressure of 1 atmosphere and a temperature of around 300 K for the air in your room), there are many microstates (in this example, there are many possible arrangements of positions and momenta of oxygen and nitrogen molecules in the room that all look macroscopically about the same). The macroscopic states that we observe are those that have the most possible microstates associated with them. There is nothing physically forbidden about having all of the air in your room just in the upper 1 m of space; it's just that there are vastly more microstates where the air is roughly evenly distributed, so that's what we end up seeing.

Crucial to actually calculating anything using this idea, we need to be able to count microstates. For pointlike particles, that means that we want to count up how many possible positions and momenta they can have. Classically this is awkward because position and momentum are continuous variables - there are an infinite number of possible positions and momenta even for one particle. Quantum mechanically, the uncertainty principle constrains things more, since we can never know the position and momentum precisely at the same time. So, the standard way of dealing with this is to divide up phase space (position x momentum) into "cells" of size h^d, where h is Planck's constant and d is the dimensionality. For 3d, we use h³. Planck's constant comes into it via the uncertainty principle. Here's an example of a typical explanation.

Here's the problem: why h³, when we learn in quantum mechanics that the uncertainty relation is, in 1d, (delta p)(delta x) >= hbar/2 (which is h/4 pi, for the nonexperts), not h ? Now, for many results in classical and quantum statistical mechanics, the precise number used here is irrelevant. However, that's not always the case. For example, when one calculates the temperature at which Bose condensation takes place, the precise number used here actually matters. Since h³ really does work for 3d, there must be some reason why it's right, rather than hbar³ or some related quantity. I'm sure that there must be a nice geometrical argument, or some clever 3d quantum insight, but I'm having trouble getting this to work. If anyone can enlighten me, I'd appreciate it!

UPDATE: Thanks to those commenting on this. I'm afraid that I wasn't as clear as I'd wanted to be in the above; let me try to refine my question. I know that one can start from particle-in-a-box quantum mechanics, or assume periodic boundary conditions, and count up the allowed plane-wave modes within a volume. This is equivalent to Igor(the first response post)'s discussion of applying the old-time Bohr-Sommerfeld quantization condition (that periodic orbits have actions quantized by h). My question is, really, why does h show up here, when we know that the minimal uncertainty product is actually hbar/2. Or, put another way, should all of the stat mech books that argue that the h³ comes from uncertainty be reworded instead to say that it comes from Bohr-Sommerfeld quantization?

A mini book review

Recently I acquired a copy of Electrical Transport in Nanoscale Systems by Max Di Ventra, a new textbook aimed at graduate students. I haven't yet had time to read through it in detail, but what I've seen so far is impressive. The book provides a thorough intro to various formalisms appropriate for understanding nanoscale transport, including the usual stuff (Drude, Kubo, Landauer-Buttiker, nonequilibrium Green's function (NEGF)) and other sophisticated approaches that focus on transport fundamentally as a nonequilibrium quantum statistical mechanics problem (dynamic density functional theory, a hydrodynamic approximation for the electron liquid, and a detailed look at the interactions between the electrons and the ions). I also appreciate the effort to point out that truly nanoscale systems really are more complicated and different than "ordinary" mesoscopic systems. The only significant omission (intentional, in large part to avoid doubling the size of the book) is a comparative lack of discussion of strong correlation effects (e.g. Kondo physics). (A good complementary book for those interested in the latter topic is that by Bruus and Flensberg.) It's not exactly light entertainment, but the writing is clear and pedagogical.

Update: By coincidence, Supriyo Datta just put up a nice long review of the NEGF approach. He also has a full book-length treatment written with a very pedagogical focus.

(For those curious about my own book efforts, it's slowly coming along. Slowly.)

Science funding.

This article confirms my previous impressions, and is very depressing. This past week the government promised roughly 200 years worth of the entire NSF annual budget to bail out the banking system. Since 2003 the US government has spent another 200 years worth of the the entire NSF annual budget in Iraq. After two years of "level funding", and the certainty that there will be no real budget passed before the election, what we really need is the prospect of another year of frozen budgets.

In related news, I've come to the realization that my research program is "too big to fail".

Update: I might as well put all of my nonscience stuff in one posting. Looking at the text of the proposed financial bailout bill here, I am aghast because of this section:

Decisions by the Secretary pursuant to the authority of this Act are non-reviewable and committed to agency discretion, and may not be reviewed by any court of law or any administrative agency.

Let me get this straight. The Secretary of the Treasury gets incredibly broad authority to use up to $700 billion to prop up the financial markets in essentially any way he decides is appropriate, and his decisions are explicitly not reviewable ever by anyone, including the judicial branch?! I'm no lawyer, but isn't this, umm, absolutely insane?

Because I'm a big musical nerd...

... I couldn't pass this up. Very well done, though someone should point out to the Obama supporters behind this that things didn't work out too well for most of the characters singing this in Les Miserables.

I will return to actual physics blogging soon, once the immediate disarray settles out.

Ike follow-up

Well, that was interesting. Thankfully we're all fine and our house is undamaged. The prospect of being without power for an extended period continues to suck, to put it bluntly. 90 degree weather, near 100% humidity, and no air conditioning or refrigeration. On the plus side, my university still has power and AC. On the downside, they've disabled access (card keys) to most buildings and water service (i.e. sanitary plumbing) is spotty on campus.

Hurricane Ike

Hello - for those readers who don't know, I live in Houston, which is about to get hit by Hurricane Ike. I'm hopeful that this won't be a big deal, but there's always the chance that I'll be without electricity for a few days. So, blogging may be slow. In the mean time, check out this cool site for following tropical storm systems, and this explanation of how hurricanes are heat engines.

Ahh, the Gulf coast.

You know, I lived the first twenty-nine years of my life without having to pay close attention to stuff like this.

Important online resource

The internet is definitely the best way to keep up with current events. Check here often (look at the link text). (Thanks, Dan.)

Final Packard highlights + amusing article

One of my former professors, Michael Peskin, has a nice article about why the LHC will not destroy the earth. He taught me graduate-level mechanics, and my brain still hurts from his take-home final.

A last few things I learned at the Packard meeting:

• The stickleback is a very useful fish for addressing the question, if natural selection removes variation in phenotypes, then why do we still see so much variation?
• There are structures on the membranes of many cells (the primary cilium; the protein known as rhomboid) that seem to have really profound effects on many cellular processes. Understanding how and why they do what they do demonstrates why systems biology is hard.
• It may be possible to do some kind of "safe" cryptographic key exchange based on functions that are not algebraic (as opposed to usual RSA-type encryption which is based on the asymmetry in difficulty between multiplication and factorization).
• There are deep connections between random permutations and the distribution of the number of prime factors.
• It's possible to run live small animals (zebrafish, c. elegans) through microfluidic assay systems in massively parallel fashion.
• Stem cell differentiation can apparently be influenced by the mechanical properties (e.g., squishy vs. hard) of the substrate. Weird.
• Artificial sieve structures can be very useful for electrophoresis of long segments of DNA.
• There may be clever ways to solve strongly correlated electronic structure problems using tensor networks.
• Natural synthesis of useful small molecules (e.g., penicillin, resveratrol) is pretty amazing. Makes me want to learn more about bacteria, actomycetes, and fungi.
• By clever trading of time and statistics for intensity, 3d superresolution imaging is possible under some circumstances.
• DNA can be used as a catalyst.
• Some bacteria in biofilms secrete molecules that look like antibiotic byproducts, but may actually serve as a way of carrying electrons long distances so that the little buggers far from the food source can still respirate.
• Virus chips are awesome.
• Don't ever get botfly larvae growing in your scalp. Ever.
• Tensegrity structures can be very useful for biomimetic machines.
• Sub-mm arrays are going to be a boon for astronomy.
• It looks like much of the Se and Br in the universe was actually produced by the same compact object mergers that give short gamma ray bursts.
• Dark energy remains a major enigma in physics and astrophysics. It's a big one.
  

Packard highlights

Some things I learned at my final Packard meeting:

• The density of stars in a globular cluster is just absurd - something like 10⁴-10⁶ stars in a volume 10 ly on a side. Wow.
• The joint between the stem and base of a wine glass is a perfect lens for demonstrating the types of Einstein rings that one sees in gravitational lensing.
• In the protoplanetary disk phase of solar system formation, elements get mixed on very rapid timescales (like around 1000 years).
• Bacteria are much better at using ⁴⁰Ca in their metabolism than ⁴⁴Ca, and it's not at all clear how this works kinetically.
• 3-5 million years ago, in the early Pliocene, the global climate is a good test case for comparison with global warming models. Bad news for me: if the trends can really be mapped onto today, the hurricane rate is likely to increase by a factor of two.
• Using isotopic analysis (!), it is possible to put an error bound on how many people the lions in the Fields Museum actually ate: 41 +- 11. Anecdotal evidence had put the number between 15 and 135.
• We're all going to be able to get our genomes sequenced very soon, since the rate at which DNA can be sequenced (base pairs per day, for example) has gone up by five orders of magnitude in the last five years.

More later....

Packard meeting 2008

I'm in Park City for my last annual meeting as a Packard Fellow. As I've said before, I can't speak highly enough of the Packard Foundation. Their support has jumpstarted or otherwise contributed to pretty much my entire research program, and through their annual meetings I've gotten to know meet some fascinating people and hear excellent talks in the sciences, mathematics, and engineering. This is a particularly special meeting because it's the 20th anniversary of the Packard fellowship program, and they've invited back all the previous fellows. I'll try to post some highlights over the next few days.

Follow-ups

First, following up on my earlier post about the field effect.... I'd seen some of this before but had some really good conversations at the workshop in Japan last week about electrochemical gating. The field effect, as I'd said, is a great way of tuning the density of charge carriers at a surface without the disorder associated with chemical doping. By cranking up some gate voltage you can in some sense just rely on the attraction of opposite charges to accumulate carriers, for example. One major limitation to this technique, though, is the amount of charge that you can really get in there using reasonable dielectrics between the gate and the surface of interest. A given insulator can only take a certain amount of electric field across it before leakage current (and eventual breakdown due to damage from "hot" electrons) starts. Calling that limiting field E_max, you can find the maximum gated charge density to be \epsilon_0 \kappa E_max, where \epsilon_0 is the permittivity of free space in SI units (8.85 x 10^-12 Farad/m) and \kappa is the (unitless) relative dielectric constant. If you've got a really good oxide you can get this product up near 10¹³ carriers per square cm. Usually there is a tradeoff - materials with a big \kappa have a smaller breakdown field. One way around this is to use electrochemical gating. Instead of a dielectric, use either a polymer electrolyte or an ionic liquid. If you don't care about speed of response, this is a great idea because you can get a layer of counterions right next to the surface of interest. As a result, you can accumulate carrier densities exceeding 10¹⁴/cm². That's a huge density that can let you do some fun things even in strongly correlated materials, where you're now talking about adding or removing more than one carrier per unit cell.

A very brief follow-up to my post about the weather: Aww, not this crap again. Hurricane Gustav is really starting to look like a potential annoyance. Here's hoping that it hits neither New Orleans nor Houston.

Sad. Just sad.

According to a news article in Nature, there are now only four PhD scientists left at Bell Labs doing basic research. Four. Leaving aside that I know those guys personally, we should all be saddened by this.

I know that in industry there's always a tension between the immediate company bottom line and longer term investment. I can't help but wonder, though, in these days of institutional investors, mutual funds, and huge executive compensation, if we've really screwed up. Let me put it this way.... Once upon a time there were long-term investors who bought, e.g., AT&T, and really cared about whether AT&T was going to be competitive in ten or fifteen or twenty years. Now most stock is held by institutional investors and mutual funds who really don't care whether AT&T exists in ten years - they just care that there's something with a risk/reward profile like that in ten years. Furthermore, the executive compensation system is designed to massively reward short-term results (how much is this quarter's rate of growth greater than last year's? Note that making a big profit isn't enough - you have to be increasing your profit rate, not just the absolute amount of money the company makes.). As far as I can tell, we have effectively removed much of the economic incentive for long-term investment. No wonder any research and development with a 10-year horizon is almost gone from the American technological landscape. The only exceptions, as is often the case, are companies with so much money that a small research investment is negligible and can give decent PR, like Intel, Google, and Microsoft. Yeah, I know that HP Labs still exists, and I know that IBM still has people playing with STM, and I know that Exxon and Dupont and 3M have lots of talented chemists, but it looks like the days are largely gone of having a staff with a critical mass of tens of physics and chemistry PhDs doing cutting edge long-term research in an industrial setting.

Slow blogging....

I'm off to Japan for this week, primarily to speak here, and secondarily to guarantee that I'm a jetlagged wreck for the first week of classes. So, unless I do some Lost in Translation blogging, it'll be a quiet week here.

Cryptophysicists

I think that we need to coin an official term, "cryptophysicist", to describe people who do physics research outside the mainstream. Ronald Mallett is an example of a credentialed cryptophysicist - he wants to build a time machine using circulating optical beams. His tragic motivations aside, this is a scientifically wacky idea - the energy density that you would need in the beams to produce any significant distortion of spacetime is completely unachievable with foreseeable equipment. On the theory side, Harold Puthoff is another example. Puthoff wants to explain things like inertia in terms of interactions between matter and zero-point fluctuations of the electromagnetic field. Mainstream theorists consider this to be a wacky idea for a long list of reasons.

One major difference between cryptophysicists and cryptozooligists is that the public is generally able to perceive that the latter are outside the mainstream. Everyone knows from daily experience that there probably aren't yeti or sea monsters hanging around. Modern physics is abstracted enough from everyday lives and intuition, though, that many people, including some journalists, honestly can't tell when someone's waaay out there. Also, the concept of the lone genius toiling away in obscurity fighting The Scientific Establishment, which makes for good TV, sounds better when applied to a garage tinkerer than to someone camping out looking for the chupacabra. Still, occasionally the biologists do get to have fun with media coverage of this stuff.

The US election and science

For anyone interested in the US presidential candidates' positions on science, I recommend this NPR piece from today's "All Things Considered". What I find most revealing is near the end. Obama supports the goals of the America COMPETES act, which (among other things) was intended to double support for basic science research over the next several years. McCain does not consider science research to be as high a priority, given fiscal constraints. Bear in mind that as a percentage of GDP the US spending on physical science research has been falling for decades, and we've also witnessed the near-death of industrial long-term research in the sciences. I'm not trying to start a political flamewar here - I just wanted to point people to this information.

Update: From the Department of the Obvious, this article from USA Today about general science literacy and cultural perception in the US. How depressing. 44% of those surveyed couldn't name a single scientist, living or dead, that could be a role model for young people. Wow.

Whoa.

This article (thinks, Incoherent Ponderer, for pointing this out and your insightful post) is really distressing. Prof. Plummer is a class act and chaired a session of the APS Focus Topic that Eric Isaacs and I put together for this past March Meeting. I hope Tennessee is able to find the resources to support him fully.

Random samples

Three little items....

First, the Foundational Questions folks have announced their funding recipients. These grants, intended for fundamental questions in physics and cosmology, are supposed to target topics "unlikely to be otherwise funded by conventional sources". I'm a bit skeptical about that, since it sure looks like a number of these people are getting funded for topics that sound just like their regular research. Still, I do think it's a good thing to put some resources into real foundational questions. For the condensed matter people in the audience, our token representation on the list is Subir Sachdev, who is extending his theory formalism to cover black holes (!), and Keith Schwab, who is going to do true quantum mechanics by building micromechanical systems that exist in a quantum regime.

Second, this paper is one of the more bizarre things I've seen on the arxiv lately. It's from some folks trying to find efficient ways to compute pagerank numbers (useful in search algorithms for the web). They claim to have a Schroedinger-like equation that describes the pagerank. I was intrigued, in part because of all the lame joke opportunities this suggested. Funky.

Lastly, it's disappointing to read articles like this one and this one. I don't know what's more sad - that the the Holmdel Bell Labs site is being sold to developers, or that the Wall Street Journal can run multiple long articles about the discord and tribulations at the top of Alcatel-Lucent and not even mention Bell Labs. I can't help but think that the US will really miss industrial long-term research.

Ahh, the weather.

It's that time of year again, when we get a brief break from high-90s (F) heat and high humidity by having a tropical weather system blow through the area. Hopefully this will bring us some much needed rain, but not too much. It's interesting to watch the evolution of computer models here, and also to keep track of historical trends. I never had to think about this stuff growing up in Pennsylvania....