Money

A very brief post. The new estimate for the cost of ongoing military operations in Iraq and Afghanistan is approaching $10B/month. For the foreseeable future. That's the entire NSF annual budget every 17 days. Remember that service on the national debt is also on the order of $20B/month. And the national debt is increasing at a rate of more than $2B/day. Some say to properly normalize those numbers you must remember that the GDP of the US is on the order of $12T/yr. Of course, it's also important to consider that 20% of all tax revenue in the US now goes to paying the debt service. How one can argue that this is all healthy is beyond me.

The second topic - polarons and molecular IVs

A second interesting discussion going on right now concerns hysteresis in molecular electronic device current-voltage characteristics. There have been a number of papers that have reported hysteretic IV curves in molecular systems, where applying a high bias can make the system undergo a transition from a low-conductance state to a higher conductance state. That higher conductance state persists until the bias voltage is cycled back down to some value below the turn-on voltage. This sort of hysteresis is interesting from the practical perspective: if the high/low conducting states are long-lived, one could imagine making a memory or logic out of devices with these properties. The main scientific question, then, is what is the underlying mechanism for this conductance switching?

One candidate that has been suggested by a number of people is polaronic. A polaron is a charge carrier accompanied by a geometric distortion of the charge carrying medium. The basic idea is that one can start with a neutral molecule, transfer an electron onto that molecule, and once that electron is there, the molecule could distort in such a way as to greatly lower the total energy of the system. The result is that the molecule could trap that additional electron via a geometric deformation. If the neutral and charged states of the molecule have significantly different couplings to the source and drain electrodes, this kind of trapping could conceivably lead to hysteretic switching between conductance states. Such a strong electron-vibrational coupling would basically make the effective on-site repulsion, U (for the no vibrational coupling case), be renormalized downward, all the way to a negative value.

This problem is interesting because it's fundamentally non-perturbative, at least in the electron-vibrational coupling, and generally non-equilibrium, too. Theorists have therefore been arguing about the right way to solve this system. As always, the whole point of this kind of theory is to come up with a toy model that includes all the essential physics and omits nothing of importance, and then use some method to solve it. If one leaves out the coupling between the electronic level and the leads, and considers just a single electronic level, this problem can be solved analytically, with no hysteresis showing up. One can include the coupling to the leads in some limit, and solve using Hartee-Fock techniques, again finding no hysteresis. One can choose a different set of limits, and find hysteresis; and finally, one can do a more sophisticated treatment of the nonequilibrium aspects and find telegraph-like switching rather than hysteresis. The big question is, which if any of these models are really relevant to the regime of experiments? It's highly likely that much switching in experiments really has to do with the geometry of the molecule-metal bond, rather than anything this exotic. Of course, that doesn't mean it's not worth trying to examine this question deliberately through experiments....

Two interesting condensed matter debates

In the past couple of weeks, two interesting debates have come to my attention in condensed matter circles. The first has to do with electronic transport in graphene, and isn't really a debate - more of an interesting observation having to do with weak localization, a specific quantum correction to the classical electrical conductivity. Consider an electron propagating through a solid, scattering off of static disorder (lattice defects, grain boundaries). Feynman tells us that we have to add amplitudes for all possible paths through the material, and then square the sum of those amplitudes to get a transmission probability, assuming that all the paths add coherently. Some relevant trajectories include closed loops, that take the electron back past its starting point. For each loop like that, there is another trajectory with the loop traversed in the opposite direction. In the absence of spin-orbit scattering or magnetic fields, those loops and their time-reversed conjugates all add in phase and interfere constructively. The result is an enhanced (nonclassical) probability for the electron to back-scatter, leading to an enhanced resistance. Now, if one threads magnetic flux through those loops, electrons traversing loops in opposite directions are phase shifted relative to one another, and the constructive interference is broken. The weak localization enhancement of the resistance is suppressed at high magnetic fields, and the result is a magnetoresistance, with a field scale set by the size of the typical coherent loop. This is one of the main ways people estimate quantum coherence lengths in conductors.

What does any of this have to do with graphene? Well, here Andre Geim and coworkers look at transport in single graphene sheets, and find that weak localization is essentially absent. It turns out that the particular electronic structure of graphene implies that one can get the effect of a magnetic field if the graphene sheet isn't really flat. (For the experts: this has something to do with a pseudospin involving two equivalent sublattices on the sheet, and the breaking of that symmetry by roughness. I don't really understand this, so please let me know if there's a clear writeup about this somewhere.) Conversely, in a new paper de Heer and co-workers grow graphene epitaxially on SiC wafers, and do observe weak localization. Interesting - this seems to imply that the material grown by de Heer is in some ways intrinsically superior to that prepared by other methods. This is also roughly confirmed by the mobilities (25 m^2/Vs in de Heer's, 10 m^2/Vs in Geim's).

I'll hit the second discussion in the next post....

Science magazine and retracted papers

Since Science isn't going to run my letter to the editor, I'll just vent about it here. In last week's issue, Science ran a news article about the distressing tendency of retracted papers to linger on in the literature, sometimes still picking up citations long after the retraction. In the old days of strictly print journals, the excuse was that someone could stumble upon the original hardcopy of the retracted paper and not realize that it had been withdrawn. Now, though, the problem continues even in on-line versions of the papers. The Science reporters had expressed surprise that retraction notices don't always catch everyone's attention.

I find this very ironic, because Science has been part of the problem. Back in the dark days of late 2002, the Beasley Commission officially released their report, demonstrating beyond a shadow of a doubt that Jan Hendrik Schon was a complete fraud, and that his major papers needed to be retracted. The retractions happened almost immediately. Fast forward to December 2003, when two students writing final papers for my course mistakenly cite Schon's Science papers, despite their retraction over a year before. Why did the students not realize that the papers had been withdrawn? Because google had linked directly to the pdf versions of the papers, and Science had not marked up the pdf files to indicate the retraction. So, I used the on-line feedback form to tell Science about this problem. No response beyond an automated "Thank you for your email" formletter. Fast forward again to December, 2004. Again a student cites a Schon Science paper in the final paper for my course. Over two years after the fact, and the pdf files still don't indicate the retraction. I sent another letter, with a similar response.

Science has finally fixed this problem sometime in the intervening 15 months or so. I just find it funny that they seem to shift the blame onto their readership, when they themselves aggravated this problem by being too lazy to fix their pdf files for over two years. For Pete's sake - we're only talking about a handful of papers. It would've taken all of ten minutes to append the retraction to each file. Ahh well.

Tenure

I recently found out that I'm getting tenure. Hooray!

It is strangely anticlimactic, and I think I know why. When you get your PhD, it happens at a well-defined moment. There's a defense, applause, a document that gets signed, etc. Tenure is much more diffuse. Months ago I submitted my "package" - my CV, some representative reprints, a statement of my research results and plans, etc. My department then sent out for external letters, and eventually had a vote of the tenured faculty on my case, as well as that of a couple of colleagues. The whole thing then got pushed forward to the dean's level, and eventually to the university's promotions and tenure committee. Fall turned to spring. Eventually I heard back positively, meaning that I got a letter telling me that in another month the board of trustees will give this there seal of approval, and then as of the next fiscal year (July 1), I'll be an associate professor. So you can see that the tenure transition is much more adiabatic, if you will. Day to day, nothing changes, though it's certainly nice!

Bell Labs and industrial research

Well, it's finally happened: my friends at Bell Labs are going to be learning to speak French, since Lucent and Alcatel are merging (as "equals", of course). What this means for Bell Labs is unclear. Since they do a fair bit of DOD work, at least part of the labs will have to be operated by an American-owned spinoff of some kind. This would further fragment the research organization, which was already split by the spinoff of Agere (motto: Welcome to Agere, Bell Labs researchers - here's your lay-off paperwork.) and the hemorrhaging of personnel, particularly in the physical sciences.

The continued shrinking of industrial research in the US is extremely depressing. There are things that can be done in an industrial research environment that just don't work well at a university. With the prevailing attitude that any research directed at long-term (say > 5 years) goals is effectively a waste of money unless it pumps up the stock price right now, it's no wonder that we're facing tough times in terms of competitiveness. I believe this is the equivalent of "eating the seed corn."

How to spot bogus science

There is a great, free article in the Chronicle of Higher Education from back in 2003 that has just come to my attention, about how to spot bogus science. The article is by Bob Park, who writes a weekly "What's New" column that used to grace the APS webpage.

This is an important read, particularly as there seems to be a steady flux these days of news items that seem pretty weird to me. For example, these folks are a bunch of cold fusion advocates, who last week put out a big press release about how happy they are that Martin Fleischmann is joining their product development team. For another example, take this announcement by the European Space Agency that their researchers think they've spotted a funny gravitomagnetic effect near rotating (low Tc) superconductors. The data look pretty marginal to me, and I think it's pretty indicative that on the one hand they put out a big, glossy press release, while on the other hand they submitted the paper to Physica C. I don't want to knock Physica C too badly, but they aren't exactly a high impact journal. At least the ESA researchers are using the peer-reviewed literature, though, and seem to be reasonably careful. They need to be, though - they're claiming big deviations from general relativity, and extraordinary claims require extraordinary evidence.

Wow - a really surprising result!

The cover story on the latest issue of Phys. Rev. Letters is quite surprising! A group in Italy have performed what a colleague of mine called a "hero experiment": they've taken linearly polarized light, and passed it through a 3 m long ultrahigh vacuum cavity in a rotating 5.5 T magnetic field. The shocking result is that they observe that the polarization of the light rotates because of the magnetic field. Basically they've measured a magnetic dichroism of vacuum. This is unexpected, and ordinarily it really shouldn't happen - it implies that the photons from their laser are interacting in a very nontrivial way with the (virtual) photons that make up the magnetic field. One way this could happen would be via a two-photon scattering process involving a never-before-seen neutral, spinless, very low mass particle. The paper is also remarkable for being the only PRL I've ever seen that's over the four page length limit of the journal, and for appearing without some enormously overblown marketing in the form of press releases.

This could be a very very big deal if confirmed. There is already one idea for an independent test of this. I would imagine that it would have major astrophysical consequences, too. After all, the hypothesized mechanism would lead to an effect quadratic in magnetic field, and the fields around astrophysical objects like neutron stars can be millions of times bigger than the field used in this experiment....

This week in cond-mat

Slightly delayed because of the joys of grant proposals, here is this week's installment of my quasi-periodic snippets of things I find interesting on the arxiv preprint server....


cond-mat/0603598 - Siemons et al., Origin of the unusual transport properties observed at hetero-interfaces of LaAlO3 on SrTiO3
This paper is interesting for a couple of reasons. First, the author list includes some luminaries in the field, including Ted Geballe, Mac Beasley, and Walt Harrison. They're all extremely nice guys, and Walt literally wrote the book(s) on electronic structure calculation methods. It's great that these folks are not just still active, but really pushing new ground, at a point in their careers when many full professors decide to kick back. Second, this paper reports data on a relatively new material system, a heterojunction between two oxide materials. Like the GaAs/AlGaAs case, the conduction band offset between the two materials leads to the formation of a potential well right at the interface, so that electrons can be trapped there in a two-dimensional layer. This result studies electronic transport in those layers, and tries to address the question of where the free carriers come from, given that the materials are ideally not doped.

cond-mat/0603482 - Pickett, Design for a room temperature superconductor
Bonus points for the provocative title. This paper (part of a commemorative volume in honor of Vitaly Ginzburg), looks at MgB2, a superconductor that is not a copper oxide, but nonetheless has a transition temperature of nearly 40 K, and tries to argue from that material what would be necessary to have (phonon-mediated) room temperature superconductivity. Thought provoking, and with references to good MgB2 literature for those interested in how that material was discovered to superconduct at the shockingly recent date of 2001.

APS March Meeting

No cond-mat update this week. I just returned from the March Meeting of the American Physical Society, that annual opportunity to get together with 7000 of my closest condensed matter physics colleagues and stay in over-priced hotels with malfunctioning wireless internet access. The meeting was good - I'll mention just a few observations:

• There was a particularly nice session on the recent transport experiments in graphene that I've mentioned in previous posts. The talks were interesting, and there were rumors of cool new data not yet in print (i.e. observation of the quantum Hall effect in graphene at room temperature (!!) and 30 Tesla).
• There was an invited session on topological quantum computation with a couple of talks that were almost utterly incomprehensible to the nonspecialist.
• The fire marshals kicked a bunch of people out of a ridiculously small room housing a single-molecule electronics talk, and closed the door right in the face of a Nobel laureate, who took that with good grace.
• Speaking of single-molecule devices, there continues to be lots of interest and lots of effort in that area - a very exciting topic I should write more about later.
• Apparently, if you're a big enough name in a given field, you can coin new vocabulary and assume that everyone will figure out what you mean.

I'll write more about some science later.

This week in cond-mat

Here's a couple of preprints that I've found interesting in the last week. Note that I'm not going to be surveying the published literature as much, since there are other resources such as the Virtual Journal of Nanoscale Science that do an excellent job of that (though they miss papers in ACS journals, which increasingly contain results at the border between chemistry and condensed matter physics).

cond-mat/0603173 - Manfra et al., Reentrant anisotropic phases in a two-dimensional hole system
I'm not writing about this one just because Mike Manfra and I used to share an office at Bell Labs. Two-dimensional electron gases (2degs) have been a workhorse physical system over the last 25 years, showing a number of fascinating many-body pieces of physics, including the integer quantum Hall effect (which has led to the definition of the standard Ohm!), the fractional quantum Hall effect (a demonstration of a correlated electronic state that has excitations with fractional quantum numbers, including fractional charge), apparent zero-resistance states under microwave illumination, and interlayer quantum coherence in bilayer electron-hole systems. Another weird effect observed recently is the onset of big anisotropies in the electrical resistance of such 2degs in very clean material at very low temperatures. The explanation for this spontaneous anisotropy is generally thought to involve the electronic system breaking up into some kind of stripes. With the recent development of new high quality two-dimensional hole systems, now one can test this idea. In the new cond-mat paper, Manfra et al. find that the anisotropies are very different in the hole system than the electronic analog, and discuss how details of the single-electron states (like the presence of strong spin-orbit scattering in the hole case that is absent in the electron case) can matter greatly.

cond-mat/0603108 - Badzey and Mohanty, Coherent signal amplification in bistable nanomechanical oscillators by stochastic resonance (also Nature 437, 995 (2005)).
Stochastic resonance is a neat phenomenon, when nonlinear systems can sometimes exhibit improved signal to noise when additional noise is introduced deliberately(!). This paper is a cute implementation of this idea, using bistable nanomechanical resonators as the nonlinear element. When you think about it, bistability (the resonators seem to have two competing, well-defined oscillatory states, one with high amplitude and one with low amplitude) is about as nonlinear a response as you can get. While some of this group's earlier work with these resonators has engendered some controversy, this paper is very pretty.

HIgh Tc: where are we

As I said in my previous post, Nature Physics has run a fascinating piece surveying a number of theorists about the current state of the high Tc problem. I encourage you to read it, and I'll summarize very briefly for those without access to the journal. Things that everyone seems to agree on:

• The symmetry of the superconducting pairing is d-wave.
• The parent compounds of the high Tcs are "Mott Insulators". In the absence of strong electron-electron interactions, these materials would be metals; however, strong on-site repulsions on the coppers (so that no copper site d-orbital can be doubly occupied) lead to insulating behavior, and antiferromagnetic ordering at low temperatures.
• The normal phase above Tc for the optimally doped compounds is really weird. It appears that the normal concept of quasiparticles fails there. When superconductivity is killed by whopping huge magnetic fields, the weirdness of the normal state persists down to T=0.
  
• Understanding the normal phase is probably a good idea for understanding superconductivity.
• There are signs, even within the superconducting phase, that there can be some kind of charge ordering ("stripe order" is a phrase that is used a lot).
• In the underdoped compounds, there is a pseudogap in the density of states that exists to temperatures far higher than Tc.
  

Things that some people agree on:

• The resonating valence bond picture accurately describes the superconducting phase; there is something called a spin liquid, and the pseudogap essentially corresponds to the formation of some kind of pair-like correlations without global phase coherence.
• The pairing mechanism is purely electronic (as opposed to phonons in conventional superconductors).
• The superconductivity is a general feature of doped Mott insulators.
• There are quasi-2d Mott insulators that do not superconduct at all when doped.
• There is no quantum phase transition (that is, at T=0 as a function of, say, doping) in these materials.
• There is a quantum phase transition in these materials, and therefore there is a well-defined (if very hard to detect) breaking of symmetry when going from the strange metal phase to the pseudogap phase.
• The stripe order is crucial, and competes with superconductivity.
• The stripe order is incidental and unimportant.

What I think is interesting, as a bystander:

• Everyone has their favorite handful of experiments that they treasure, and is appreciative that the materials growers have gotten so good at making clean samples of these nasty quaternary compounds.
• Only Chandra Varma explicitly addresses the reason why copper is special, chemically, in his microscopic picture (which has almost no relation at all to simple concepts of pairing, as far as I can tell).
• Very few people bother to address the existence of electron-doped superconductivity in these systems.
• It is clear that the whole field is strongly hampered by the fact that chemical doping is a real bear at these levels - it introduces large amounts of disorder. Field-effect experiments would be great, if only they could really change the charge density by chemically interesting amounts.

The field continues to progress, though it's not for the faint of heart. The holy grail of room temperature superconductivity still beckons, though there are those who make reasonably persuasive arguments that the copper compounds are awfully special, and may be as good as it gets. For me, I'll stick to nanostructures for now.

20 Years of High Tc

There is a very interesting article in the new issue of Nature Physics regarding the twentieth anniversary of the discovery of high temperature superconductivity. In case you've been living under a rock since 1986, the high temperature superconductors are generally based on perovskite quasi-two-dimensional compounds that have extraordinarily rich (read: so complicated they're hard to understand) phase diagrams. The parent compounds are antiferromagnetic insulators in their ground state. In doped compounds (done by substitutional chemical doping at the ten percent sort of scale, which introduces significant disorder), the superconducting state is well-described by a BCS-like state with spin singlet d-wave Cooper pairs (and just establishing that firmly took years, and an enormous effort at sample growth, and several brilliant experiments).

The normal state of these materials is a real mess. At very high doping levels, the materials seem to be well-described as Fermi liquids, which is the standard picture of ordinary metals. You can think of the electrons as partially filling a band of states that look very much like non-interacting single-particle states. Excitations above the ground state look like well-defined electron quasiparticles, as demonstrated by, e.g., a resistivity that varies like the temperature squared. Near optimal doping for the superconductivity, the normal state is a "strange metal", meaning that the resistivity varies with temperature like T, implying that quasiparticles are not a sensible way to think about excitations of this material. In underdoped materials, the normal state looks like a strange metal with a "pseudogap", vaguely reminiscent of the superconducting gap in the density of states, but persisting up to much higher temperatures than the superconducting state.

The Nature Physics article is a collection of comments by a bunch of big-name condensed matter theorists. Interestingly, and I'll write more about this in a day or two, there still is suprisingly little concensus about what's really going on in these materials. Definitely worth a read!

This week in cond-mat

I'm going to try to get more serious about regularly blogging condensed matter physics issues. First, I intend to have a weekly discussion of cool results on the arxiv preprint server, and here is my inaugural attempt. Think of it as a poor man's Condensed Matter Journal Club. The Bell Labs version is fine, but their tastes run rather to the theory side for me....

cond-mat/0602623 - Troisi and Ratner, Molecular Transport Junctions: Propensity Rules for Inelastic Electron Tunneling Spectroscopy
This paper is a snapshot of a whole subfield that lies at the interface between physics and physical chemistry. The molecular electronics community has long been interested in ways of characterizing molecular layers or even single molecules by their "fingerprint" one electronic conduction. Correctly formulating a theoretical approach to electron transport through a realistic system is very challenging: this is basically a nonequilibrium problem, with both electronic and vibrational degrees of freedom driven far from thermal equilibrium. This paper shows that IETS intensities can often be strongly affected by symmetry considerations.

cond-mat/0602608 - Wunderlich et al., Coulomb blockade anisotropic magnetoresistance: single electronics meets spintronics
The anisotropic magnetoresistance (AMR) is a band structure effect relevant in ferromagnets, in which the resistance of the material depends on the relative orientation of the current and the magnetization. Large versions of AMR have recently been observed in ferromagnetic constrictions here, here, and here, as well as in dilute magnetic semiconductors here. This paper reports a very interesting experiment, in which single-electron transistors are formed from a dilute magnetic semiconductor (GaMnAs). The resulting devices show single-electron charging effects in their conduction, but strongly modified by large tunneling AMR. Neat stuff.

cond-mat/0602565 - Novoselov et al., Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
This is another great example of the work going on in a comparatively newly examined material system: electronic transport in essentially single (or in this case double) graphene layers. Because of the unusual band structure of graphene, charge carriers have an effective mass of (ideally) zero (!), which has all kinds of strange consequences. This material was first examined essentially simultaneously by about four groups (1, 2, 3, 4), three of whom spoke in a session I organized last year at the March Meeting of the APS. It absolutely blows me away that one can put single sheets of graphene down on surfaces, wire them up, and not have disorder completely bugger all the transport.

Out of gas....

Last week David Goodstein from Cal Tech came to Rice and gave a great lecture based on his book, Out of Gas, about the "end of the age of oil". The lecture was so distressing that I'm still thinking about it quite a bit almost two weeks later. Goodstein's main point is that our ever growing energy needs, coupled with the rising demand from the rest of the world (read: China and India, who for some wacky reason would like to enjoy standards of living similar to ours), make it highly highly likely that we will run out of fossil fuels sometime this century. Indeed, his one prediction is that "Civilization as we know it will end in the next 100 years, as we run out of fuel."

I know, I know - there are lots of "peak oil" nutjobs out there, but Goodstein isn't one of them. He's just a very bright guy who makes a really convincing case.

What are our options, according to him? Basically fusion (which is and might always be about 40 years away), or solar. Fission runs into trouble from problems of capacity (to satisfy 10 TW of demand will require building typical 1 GW reactors at a rate of one per day for 30 years), let along issues of fuel reprocessing.

Frankly I think the time is right for an Apollo/Manhattan Project style investment in this problem. Dumping less than 1% of the GDP ($100B, or, in better units, a few months in Iraq, or 1/3 of the annual service on the federal debt) into this per year at one or two re-dedicated national labs makes a lot of sense to me. It's much easier to invest now than when things get really desparate....

Stem cells and Jan Hendrik Schon

Unless you're living under a rock, you've heard about the scandal unfolding involving Dr. Hwang Woo Suk of Seoul National University. He is the world-famous scientist now accused of falsifying his stem cell research, the most recent paper of which had been published in Science. I want to point out something that has been entirely neglected in the media, as far as I can tell: the amazing similarity between this and the J. Hendrik Schon fiasco. For example:

* Huge impact articles in major journals, with talk of Nobel prizes.
* Multiple big-name coauthors who did not spot anything wrong.
* Progress in an exceedingly demanding field far in excess of reasonable expectations, yet attracting no suspicion at the time.
* The first hints of impropriety raised due to duplication of figures (!), a sloppy mistake virtually guaranteed to be noticed eventually.
* Immediate denial by the PI, with claims that the whole problem comes down to poor record keeping.
* Initial institutional announcements that while some particular result may be flawed, the body of work is still good, pretty much because the PI is a "genius".
* Claims by the PI in the face of mounting evidence of fraud that the results are true.
* Complete denial of any responsibility by the journal editors, who may or may not have downplayed negative referee reports because the results are potentially so important.

Interesting, eh?

The most important similarity in both cases, of course, is that they got caught - the scientific process did work, albeit slowly.

One other comment: I hate it when ethicists insist that the real problem is the lack of formal ethics training in the scientific curriculum. That is absolute garbage. Does anyone really think that Hwang or Schon didn't realize what they were doing was wrong? Does anyone really think that one more ethics course would have prevented either case? Come on. Seriously.

A long break....

Sorry for the long break. It's been a very busy time in academia. I did finally finish my 100 page review article about single-molecule transistors, though. I also spoke at the Bat Sheva Seminar on Electron Transport in Molecular Junctions, possibly the best scientific meeting I've ever attended.

I heard two striking things at the meeting. First, Europeans and Israelis were shocked at how much time Americans spend writing grant proposals. Interesting. Second, there are still real problems in our understanding of interfaces at the atomic scale, and charge transfer. There is even still debate about whether the theory prediction vs. experimental data divide is converging. On the side saying that real progress is being made are folks like Stuart Lindsay and Mark Ratner. Those arguing that there are still major discrepancies include Amir Yacoby. Fascinating discussions.

I'll discuss a couple of specific recent results next time.

Least action and non-classical paths

Here's a funky piece of physics discovered in condensed matter research that deserves broader attention because it is so weird.

So, the Feynmann-Hibbs path integral approach to quantum mechanics says that the way to calculate the probability of a quantum system starting at configuration {a} and ending at configuration {b} is to add up the complex amplitudes for all possible paths between {a} and {b}. For each path, you can compute the classical action, S, by integrating the Lagrangian along the path, and the amplitude for such a path is given by exp^(i S / \hbar). This is particularly nice because paths that extremize S end up constructively interfering (having very similar phases). So, when one passes to the classical limit (\hbar -> 0), one finds that the dominant classical trajectory for the system is the one that extremizes the action. Unsurprisingly, the trajectory that dominates is something smooth that looks like a sensible classical path (e.g. for a particle propagating in free space, it's a straight line from point a to point b).

Here's the weirdness, though. There is at least one system (quantum tunneling of spin in molecular magnets) for which the action-extremizing paths are discontinuous. In our free particle discussion, these would be analogous to trajectories where the particle's path in space looks like _____----____--__ , complete with discontinuous changes in coordinates. Such trajectories are always in the calculations (in fact, in quantum field theory you need to include paths with space-like discontinuities (!) in order to get the calculations to come out correctly), but this is the only case I've ever seen where they can be the dominant trajectories.

Intelligent design

Thank goodness the President doesn't really have much to do with setting educational practices in this country. From the transcript of his Aug. 1 press event in the Roosevelt Room at the White House:

Q I wanted to ask you about the -- what seems to be a growing debate over evolution versus intelligent design. What are your personal views on that, and do you think both should be taught in public schools?

THE PRESIDENT: I think -- as I said, harking back to my days as my governor -- both you and Herman are doing a fine job of dragging me back to the past. (Laughter.) Then, I said that, first of all, that decision should be made to local school districts, but I felt like both sides ought to be properly taught.

Q Both sides should be properly taught?

THE PRESIDENT: Yes, people -- so people can understand what the debate is about.

Q So the answer accepts the validity of intelligent design as an alternative to evolution?

THE PRESIDENT: I think that part of education is to expose people to different schools of thought, and I'm not suggesting -- you're asking me whether or not people ought to be exposed to different ideas, and the answer is yes.

Sigh. The President clearly doesn't understand that "Intelligent Design" is not science. It is unfalsefiable. It makes no predictions - it makes assertions. Saying that it deserves something like equal time with evolution in school science classes is absurd.

It's tempting to make an inflammatory statement that this demonstrates the anti-intellectual, anti-science attitude of the current administration (i.e. the "faith-based" community vs. the "reality-based" community). However, I'd be shocked if the President actually gave this that much thought; I suspect science funding and science policy (apart from firebrand issues with his base like stem cells and missle defense) rarely, if ever, cross his mind. In some ways, that's even more sad than a deliberate anti-science attitude: if it doesn't serve political ends, he just doesn't care.

The Templeton Foundation

There was an interesting story this morning on NPR about the Templeton Foundation and their efforts to fund physics research. The Templeton folks are interested in the interface between science and spirituality, and sponsor the Templeton Prize (which is intentionally larger than the Nobel). The occasion for this story is an upcoming conference at Berkeley in honor of Charles Townes' 90th birthday, sponsored by the Templeton Foundation. I know about this because, like pretty much all of my peers, I received an announcement about a Young Scholar's competition being held at this meeting.

I have no problem with increased dialog between science and religion, as long as people remember where the boundaries are. "God did it" is a rather inquiry-ending proposition to hold in a scientific investigation, so I prefer to assume that non-supernatural explanations exist for the world around me and go from there.

Anyway, the story is interesting food for thought. Physicists talked to who are skeptical of the Templeton Foundation's motives include Sean Carroll and Lawrence Krauss.