Diffusion in a weakly random Hamiltonian flow

Abstract

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.

References in corpus (2)

• Self-averaging of Wigner transforms in random media
• Quantum diffusion of the random Schrodinger evolution in the scaling limit

Cited by in corpus (9)

• A diffusion limit for a test particle in a random distribution of scatterers
• Motion in a Random Force Field
• On the theory of Lorentz gases with long range interactions
• Long time, large scale limit of the Wigner transform for a system of linear oscillators in one dimension
• Diffusive limit for the random Lorentz gas
• Relativistic diffusive motion in random electromagnetic fields
• Wave field correlations in weakly mismatched random media
• Dynamical random walk on the integers with a drift
• Stochastic acceleration of solitons for the nonlinear Schrödinger equation