Timeline for Statistical Physics of a System with Friction inside a Hot Bath
Current License: CC BY-SA 3.0
11 events
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| Apr 13, 2017 at 12:39 | history | edited | CommunityBot |
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| Feb 22, 2016 at 13:58 | comment | added | Steven Mathey | @Sina I recently read this and found it very interesting. You need to know about the Keldysh formalism though. | |
| Feb 22, 2016 at 13:58 | comment | added | Steven Mathey | @Sina The general theory of classical field theories coupled to thermal baths was worked out by Hohenberg and Halperin in this paper. It's a long, difficult and interesting to read. Learn about the Renormalisation Group first. | |
| Feb 22, 2016 at 13:56 | comment | added | Steven Mathey | @Sina Sorry, I can't think of some general book on the topic. As I said it's an open question. I learned about MSR formalism with the book of Zinn-Justin, Quantum Field Theory and Critical Phenomena., chapter 4. It is a very complete book about quantum field theory. | |
| Feb 21, 2016 at 0:36 | vote | accept | Sina | ||
| Feb 21, 2016 at 0:36 | comment | added | Sina | I see I am starting to understand the correct way to pose this question now thanks to your replies. I guess I should have asked does the time average of observables for the stoachastic ODE $\ddot{x} = -\nabla U(x) - \nu \dot{x} + R(t)$ converge to the statistical average of a system with Hamiltonian H = K + U via the equipartition theorem? Can you suggest some reading material on this? | |
| Feb 20, 2016 at 9:24 | comment | added | Steven Mathey | One way to be sure that your dynamics are conservative is to choose every individual realisation of your stochastic process to be. If $\mu=0$ and the probability that $R(t)$ does not derives from a potential is zero, then your dynamics will be conservative by construction. If you are asking if effective conservative dynamics emerge once the random noise has been averaged over, then I don't know. This is a very hard problem and a modern research topic. | |
| Feb 19, 2016 at 23:01 | comment | added | Sina | Yes but I meant newtonian mechanics with a conservative force=field that is derived from a potential that only depends on coordinate variables. Thanks for the link and the answer I will check if it is what I want. | |
| Feb 19, 2016 at 19:45 | comment | added | Steven Mathey | You never leave Newtonian mechanics. The dynamics are defined by Newton's equations. However if you compute average quantities, you must take into account the fluctuations of $R(t)$ carefully. $\langle x(t) \rangle'' = - k \langle x \rangle - \mu \langle x \rangle''$ as if $R(t)$ was not there, but $R(t)$ enters the computation of $\langle x(t) x(t') \rangle$ for example. Check out the link in my answer. | |
| Feb 19, 2016 at 19:40 | comment | added | Sina | I assume the simplest case where $R(t)$ is a Gaussian process with $0$ mean. Is the above claim that average quantities behave as if it was usual Newtonian mechanics $$\ddot{x}=F(x)$$ in the long run? | |
| Feb 19, 2016 at 19:36 | history | answered | Steven Mathey | CC BY-SA 3.0 |