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Statistics of finite-time Lyapunov exponents in a random time-dependent potential.

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>2002
<mark>Journal</mark>Physical Review E
Volume66
Pages (from-to)066207
Publication StatusPublished
<mark>Original language</mark>English

Abstract

The sensitivity of trajectories over finite-time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent λ, obtained from the elements Mij of the stability matrix M. For globally chaotic dynamics, λ tends to a unique value (the usual Lyapunov exponent λ�) for almost all trajectories as t is sent to infinity, but for finite t it depends on the initial conditions of the trajectory and can be considered as a statistical quantity. We compute for a particle moving in a randomly time-dependent, one-dimensional potential how the distribution function P(λ;t) approaches the limiting distribution P(λ;�)=δ(λ-λ�). Our method also applies to the tail of the distribution, which determines the growth rates of moments of Mij. The results are also applicable to the problem of wave-function localization in a disordered one-dimensional potential.