Getting going

The term has gotten going, and while there has been nothing major to report, in the spirit of this being a journal, time to record. Everything’s ticking along pretty much as usual, though it’s proved to be a more … um, inertia-filled term to start than usual, for some reason. But, worth remarking:

(1) Quantum mechanics started with a sudden immersion into Hilbert space. A sentence guaranteed to lose all the non-physicists bothering to read this, and some of the physicists as well. Irrespective: I teach quantum from John Townsend’s quantum book, which I have described to colleagues as ‘baby Sakurai’ (where Sakurai is a classic graduate textbook).

It plunges into what’s startling about quantum mechanics immediately with the description of some thought experiments about the spin of atoms, and the response of this spin to magnetic fields. Using this approach, within a single lecture, we had established that it was impossible to describe this spin with the standard or ‘classical’ prescriptions (the way we describe position, speed, etc) and that it was impossible to know the spin in the two different directions simultaneously. Then we set up the mathematical machinery required to start describing everything, and there we were, off on the journey into Hilbert space.

The true structure of Hilbert space is something that’s still being explored in the research world — the ‘explosion’ of research in quantum computing starting in the late ’90s, 70 years after quantum mechanics was discovered/invented shows that we’ve barely begun to figure out the structure of quantum mechanics. My own research is about how Hilbert space turns into real space for sufficiently large or sufficiently warm objects, and why nonlinearity affects this transition, and it is so so wonderfully easy to get lost in there. I do so get a kick out of introducing smart and eager students to this machinery, and the amazing Dirac notation.

(2) I had one of my advisees ask to meet me for lunch. This is an international student who is going through some blues, some of which I can recognize, and some are unique to his life, of course. But here’s this smart, sweet 18-year-old struggling with big issues of identity and of feeling neither at home at Carleton or in his own country, trying to figure out how to reconcile his ‘liberal arts’ choice for major with the notion of being a success, and trying hard in his head to justify the cost — both the true economic cost as well as the emotional ones — of being so far away from family and friends.

And while this is a difficult difficult conversation to have sensibly over lunch in a crowded student eatery, what I want to say to him is what I say to myself all the time: You’ve got to find what makes you happy, hard as that is to do. Because success, money, fame, all that is about happiness. So understand that everything you do is a choice you make about finding your happiness. And you’ve got to understand that decisions about happiness are made in the face of the fact that these are amorphous, morphing, fluid issues, almost guaranteed to later generate a sense of compromise, of loss, of regret. But isn’t it amazing that we belong to a generation, to an economic group that can focus on this issue of happiness, instead merely of survival?

Hah. My student looked puzzled but intrigued to see himself as engaged in an essential struggle, not just a heavy one. And that’s all I had for him at the moment.

(3) And a friend forwarded an obituary for our mutual teacher and hero, Dr. Bhargava.

Syllabi stories

I am struggling with syllabi for the next term. One is for Physics 120: Revolutions in Physics. It’s a light conceptual survey of physics, with a closer look at some ideas with historical, sociological and philosophical implications.

It’s a really fun course because I get to figure out a story to tell about physics. But finding the right text — and matching one’s lectures to it is a trick I am still learning. Then comes fitting the content into the time-constraints of a Carleton term, with its 70 and 60 minute teaching chunks spread over 10 weeks, with breaks, Tests and what not to be fitted in. That’s always a good exercise in editing and discovering of priorities — how long do I take to talk about quantum mechanics? Should I have an exercise on this day instead of a lecture? When should I do the ‘recap/review’ days? What’s a good time for this essay? It gets tricky! I’ve taught this course 4 times now, I think, and each time I tell the story slightly differently. This time is going to be a distinct shift, particularly because of a new text. I’m looking forward to figuring this term out.

It’s at the end of the spectrum from my other responsibility, Quantum I and II. I love that pair of 5 week courses: the content is very interesting and challenging, and increasingly critical in understanding modern technology. Even the techniques of analysis are cool! It’s also my second course with this cohort of technically-trained juniors, who I look forward to sparking. With any luck I’ll induce one or more of them to join my research team which is going to shrink dramatically since I have two graduating seniors working with me.

Anomalous behavior

Meanwhile, back at the farm, another Referee report, this time not so positive, but not so negative either. This is a paper with my old friend — and recent colleague — Arik on an unusual or anomalous effect. It had been understood that some (perhaps many, perhaps most, depending on how you count) classical systems are chaotic and on the other hand, their quantum counterparts are NOT chaotic. This perspective has changed recently when considering so-called ‘open systems’, which accounts for local and random interactions with other nearby systems, termed environmental decoherence — in this case, the quantum system can be chaotic as well. What Arik and I show is the appearance of quantum chaos in a system where the classical system is NOT chaotic, which is a cool and unusual result; the stronger part of our claim is that quantum effects are responsible for the chaos.

The interesting thing about the current argument with the Referee is that no one’s denying that we are seeing chaos in the quantum system, and that the classical system is not chaotic. We are now in the middle of a technical discussion about the mechanism by which the chaos occurs, and whether or not quantum tunneling is involved, etc. And when I am not feeling grouchy about all the questions, I’m actually happy because, as always, answering the questions means we learn something more and something deeper about the physics.

Hey, wait, isn’t that what I just said about the writing assignment? Trying to persuade someone is indeed an excellent learning experience .

Visual representation of data

I read a booklet by Edward Tufte last night as preparation for the writing seminar I am attending. As usual, whenever I re-read Tufte, I find his arguments a fascinating reminder of how the representation of data can be so crucial in analysis and persuasion. Of course, analysis is persuading yourself of the validity of your hypothesis.

The workshop itself today had some discussion about graphical representation and some about finding and using data sets of various sorts. The latter was fascinating, but in a way completely unrelated to my work as a physicist — we live in a truly data-rich world nowadays, and there’s information of various sorts that make you go ‘oh, cool, I didn’t know I could figure that out’. There was even a quick discussion of something called Swivel (which was termed the ‘you-tube’ of data, and it really is! Their tagline is ‘tasty data goodies’).

I was sitting with Josh, a mathematician, and Greg, a political scientist who is pretty quantitative and perhaps our table was getting a little obnoxious, given that we all play with numbers and graphs a lot more than many of our colleagues. Ah well.

Sort of coincidentally, I got email back from my friend Arnaldo in Brazil about a project I’ve been working on with him for, umm, let’s see, almost 5 years now, since we started it when he visited me, and I remember that my daughter had just been born that winter. We’ve generated one paper from it, and I’ve been sitting on some other results for quite a while now, since I can’t quite explain what we have. The ‘sort of’ coincidence is because one of the key points of this paper is pretty visual.

To understand this, take as fact at the moment that if you look at the difference between the quantum prediction and the classical prediction for the behavior of a system, as a function of various parameters — such as size and temperature — of the system, you get a fairly complicated relationship. And why would we care about this difference? Well, classical behavior is very different in principle from quantal, the latter is turning out to be very useful in all sorts of ways, and it would be nice to know when we crossed over from one behavior to the other.

You have to imagine here that this distance function is plotted on one axis, and the different parameters are along the other two axes — we’ll stay in three dimensions for now. And so you’ve got some weird looking surface in your 3-dimensional plot. But if you search for ‘scaling’, that is, if you rotate and squish the data in certain ways, this data collapses into a single curve. It’s a pretty dramatic effect visually, it says something deep about the way quantum and classical behavior is different and it’s not entirely clear to me why it does this. In short, a perfect thing to think about for years on end.

Here’s the ‘back’ story. The idea of looking for scaling came to me in the middle of a boring colloquium at Rice University — I remember doodling it on my notepad. I worked on testing the basic idea with my friend Bala and his student Ben, and we showed that it, in fact, worked in two systems. Since then some other people have also found that scaling exists in other systems, which was great, so I know we are not just fooling ourselves somehow. Next I asked Arnaldo if he’d like to help me with trying out new ways of testing for scaling. Turns out it still works, in fact the new way works even better, but we still can’t quite say why it works in the particular way it does. That is, why does the single curve we land up with have the shape it does?

Arnaldo’s nominally the computational expert on this, while it’s nominally ‘my’ project, that is, it’s in my field, so my being stuck is not good news. I have a very smart student, Parin, working on this, but he’s only 3 years out of high school, so …

I keep waiting for inspiration, but I might take my friend’s advice and rope in one of my competitors to see if they’d like to be a collaborator on this, in case they understand the result. That’s one of the pleasures, as mentioned earlier, of this stage of my professional life — I care more about understanding the physics than trying to hoard the credit for a paper or something. Losing the fear of competition is very liberating.

Phys. Rev. Lett. Acceptance!

Never fails to give me an adrenaline rush: The collaborative paper with Anatole and Jiang-bin that was being re-considered at Physical Review Letters got accepted. W00t!

If I estimate how many papers I’ll publish in my professional life, and the number of them that will be Physical Review Letters papers (that’s the premier journal in physics, though something like ‘Nature’ or ‘Science’, which address all the sciences, is a more prestigious place to publish) it’s easy enough to conclude that every PRL acceptance deserves a pretty major celebration.

Like every paper that gets accepted or rejected, it has its own story, including some of the best Refereeing that I’ve experienced (not kind words, that’s cool but more to the point, we got intelligent, insightful, and constructive criticism). And an interesting back-story, too on how the paper got built. This is a collaboration where I truly felt like a ‘senior partner’ guiding my very talented collaborators through calculations and analysis.

For the record, the abstract:

“Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms. “

Some day it might be fun to talk that paper through. It’s one that talks about an interesting new effect, one with experimental verification possible, and is liable to generate some interest.