Diffusion in a periodic potential with a local perturbation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Diffusion in a periodic potential with a local perturbation

Authors:	K Golden S Goldstein J L Lebowitz

Institution:	(1) Department of Mathematics, Rutgers University, 08903 New Brunswick, New Jersey;(2) Present address: Department of Mathematics, Princeton University, 08544 Princeton, New Jersey;(3) Department of Physics, Rutgers University, 08903 New Brunswick, New Jersey

Abstract:	We consider the diffusion of a particle at X_t in a drift field derived from a smooth potential of the formV+B, whereV is periodic andB is a bump of compact support. With no bump,B=0, the mean squared displacementE(t) E \|X_t – X₀\|² =D(V)t +C +O(e ^–t),>0, in any dimension. WhenB0, we establish in one dimension the asymptotic expansion $E(t) = D(V)t + \alpha \sqrt t + C + (1/\sqrt t )\sum _{n = 0}^\infty \alpha _n /t^n$ , 0, ast. Our analysis relies on the Nash estimates developed in previous work for the transition density of the process and their consequences for the analytic structure,of the Laplace transform $\tilde E(s)$ ofE(t).

Keywords:	Diffusion periodic potential local perturbation Nash estimates mean squared displacement velocity autocorrelation function
本文献已被 SpringerLink 等数据库收录！