What are the other options? Emit light / heat? Form a different crystalline structure? ...?The out-of-equilibrium problems I study basically aim to address the following question: if one dumps a load of energy in to a quantum system very suddenly, what happens? The natural conjecture is that if one leaves the system alone for a sufficiently long time, it should settle and become hot. In fact, it turns out that the story is quite a bit more complicated than that, and these kinds of questions are being studied quite a lot at the moment.
That's a really good question. And I'll attempt to illustrate it with probably the simplest example, although I apologize if this is too high (or too low) level! Let's start first by defining quite what I meant when I said
The lower axis here is the energy (E) minus the "Fermi energy" (E_F) which is defined as the energy of the highest-energy electron at absolute zero temperature (so don't worry about seeing a negative axis!). Now, lets consider a bunch of non-interacting electrons -- the electrons just float around, not seeing one-another or anything else. Of course, this isn't realistic, but we're theorists, so we can get away with thinking about such things. Imagine now that I "dump some energy" into my system by adding an electron with energy 1; what happens?
Well, we have some electrons that float around, not seeing one-another and not interacting. This means that there's no way to reduce the energy of the electron you've added, so no matter how long I wait, there'll be an electron with energy 1, and I'll have a non-thermal distribution (it'll look like the Fermi-Dirac distribution above with a jump at energy 1). In physics, we like to say that there is a conservation law -- the number of particle at each energy is conserved in this simple case. Of course, this isn't very interesting so far as everything is non-interacting and not terribly realistic. Now, what happens if we turn on interactions between the electrons in our system? Interactions may allow us to redistribute energy: if we have an electron with energy Ea and
another with energy Eb we can collide them and scatter to energies Ec and Ed provided Ea + Eb = Ec + Ed, e.g. energy is conserved. Notice now that we only really have one conservation law -- that total energy is conserved. In general, it is expected that such processes will eventually lead to thermalization (e.g., the Fermi-Dirac distribution at a suitably higher temperature, fixed by the energy we dumped into the system). Now, as a theorist, I want to test this expectation (let's call it a conjecture). So I turn to my favorite interacting model that I know how to exactly-solve (there are not many of these) and test this conjecture. What do I find? I find that my exactly-solvable model doesn't thermalize: when I inject energy into the system I do not recover the thermal distribution. What gives?!
Well, it comes down to what I previously mentioned -- conservation laws. These special exactly-solvable models are solvable precisely because they have lots of conservation laws (in fact, they have the same number of conservation laws as particles) and this puts very strong restrictions on how the particles can redistribute energy around and eventually leads to a non-thermal distribution. Figuring out what this non-thermal distribution is and how to compute the values of "measurable quantities" are serious areas of research at the moment. This comment ended up much longer than I anticipated, and I'm not sure of an adequate tldr!if one leaves the system alone for a sufficiently long time, it should settle and become hot
By this I mean that the number of particles with a given energy has a thermal distribution. This thermal distribution for electrons (or more generally, for fermions) is given by the Fermi-Dirac distribution and looks like the below for a number of temperatures
Yes, you can come at these kind of questions from both the applications point-of-view and also from a fundamental understanding point-of-view. For example, on the application side I saw a talk recently about a theoretical proposal for light-induced superconductivity in semi-conductors. There, you "dump" energy into your semiconductor by shining a laser on it, causing the fundamental properties of the material to drastically change -- realizing a superconductor in a conventional semiconductor! From the fundamental perspective, there's lots of questions that are being asked. I guess the most general question is something along the lines of "how does quantum mechanics recover statistical mechanics?" where statistical mechanics is the theory used to describe the behavior of macroscopic objects (e.g., what happens when you heat up a big chunk of metal?). Another question which I think is interesting (and related to the application side) is can one realize "new states of matter" (e.g., new properties or behaviours) by doing something out-of-equilibrium and waiting for this new steady state? Can we get behaviors which aren't realized in equilibrium? It's certainly an interesting field to be working in at the moment!