Register to reply

How go from Langevin to Hamilton

by fab333
Tags: hamilton, langevin
Share this thread:
fab333
#1
Feb19-13, 07:20 AM
P: 4
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?
Phys.Org News Partner Physics news on Phys.org
Detecting neutrinos, physicists look into the heart of the Sun
Measurement at Big Bang conditions confirms lithium problem
Researchers study gallium to design adjustable electronic components

Register to reply

Related Discussions
Langevin explnation General Physics 1
Langevin DE Differential Equations 4
Langevin to Fokker-planck? Uh oh... Classical Physics 2
Finding hamilton path prove no hamilton circuit exists Differential Geometry 0
How to pronounce Langevin in English? General Physics 4