Diffusion in a weakly random Hamiltonian flow

Details Diffusion in a weakly random Hamiltonian flow Diffusion in a weakly random Hamiltonian flow

2005-05-30

arxiv.org/abs/math-ph/0505082v1

Physics

Mathematical Physics

Scientific paper

10.1007/s00220-005-1500-9

We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to obtain error estimates for the convergence of the solution of the stochastic acceleration problem to a momentum diffusion. We also apply our results to the system of random geometric acoustics equations and show that the energy density of the acoustic waves undergoes a spatial diffusion.

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