Diffusion in a Weakly Random Hamiltonian Flow

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• 作者：Tomasz Komorowski and Lenya Ryzhik
• 刊名：Communications in Mathematical Physics
• 出版年：2006
• 出版时间：April 2006
• 年：2006
• 卷：263
• 期：2
• 页码：277-323
• 全文大小：437 KB

文摘

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.