Posted by Arjendu on January 10, 2010
Last Wednesday three of my colleagues at Carleton made short presentations on their research: Dwight Luhman talked about the lab he is building dedicated to looking for the effect of disorder on phase transitions in liquid helium, Melissa Eblen-Zayas on her work in understanding correlated electron materials, and Nelson Christensen on ‘listening’ for gravitational waves as a member of the LIGO collaborative. We will all be doing this over the next couple of weeks, at the request of the students, and I have a high bar to jump to meet the standards of the ones we’ve already heard.
I’m looking forward to it, even though I don’t need to recruit kids to my group quite as much as I usually have to around now. In fact, not at all. A funny thing’s happened this year, and more particularly this term: I have possibly too many students showing up wanting to work with me. In general I’ve had reasonable luck with research students, and enjoy the collaboration. But rarely do as many show up as the six that did in the first 4 days, and some of these have been talking physics with me for a few weeks or even a few months by now.
We should be able to make some headway into the projects that I currently find most compelling, which are all related to trying to understand what happens in the land between a system behaving completely classically and one behaving completely quantum-mechanically. This is a fundamentally fascinating question from me. That’s because those two kinds of behaviors can be totally different particularly when the system is nonlinear. For example, the classical system could be a chaotic ratchet or have persistent patterns, the quantum system could be a completely different kind of resonant ratchet, and how we get from such classical behavior to the corresponding quantum is not at all clear.
Does the change happen smoothly? Non-monotonically? Are there hills and valleys? What is the parameter landscape? We know it’s affected by the size of the system, the temperature and environmental effects, and by the nonlinear dynamics, so it’s a multi-parameter landscape. What sorts of possible ways are there are navigating in this landscape?
To attack all this you need just enough understanding of a handful of fairly tricky mathematical models of physics: Possibly Stratonovich calculus for noisy systems, Hilbert Space manipulation facility, familiarity with density matrices, dynamical systems theory. Once you got that, you should be able to either analytically or numerically solve for the dynamics of a particular open nonlinear system via the stochastic Schrodinger equation and/or the Lindblad formulation. My putative student has to be good enough at all this that I trust what she reports, but has to get through the relevant background material fast enough that some sort of big project can be tackled over the summer.
This year I’ve got what seems like a handful who I think could easily get ‘just enough’ of the above by this summer, and I’m pleased as punch. There are enough of these gung-ho students that I’m going to have to arrange a group meeting rather than meet with them individually.
Apart from long-term projects, I also have a very immediate deadline. I’m scheduled to give a talk at the University of Toronto at the end of February and there are some ideas and results that I’d love to wrap up and present there. Given everything else that is going on with teaching and administrating, this is going to make for a very full term. Onward!