Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How go from Langevin to Hamilton

  1. Feb 19, 2013 #1
    I have a system described by the Langevin equation

    da/dt = - dF/da* + r

    where a are complex amplitudes of electromagnetic modes (and r is the white noise).
    How if F was real, it would be the Hamiltonian of the system, but in my case (and in general),
    F is complex (because the a are complex themselves).
    So F cannot be an Hamiltonian.
    How can I obtain a Hamiltonian formulation of this problem?


    P.S.: my first idea was to write to separate equation for the real and imaginary parts of a.
    But in this case I obtain two Hamiltonian, both depending on both Re[a] and Im[a],
    so which is the Hamiltonian of the system?
    If e.g. I want to use a Gibbs measure for a, what I must use?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted