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

Schomerus, H. and Titov, M. (2002) Statistics of finite-time Lyapunov exponents in a random time-dependent potential. Physical Review E, 66. 066207.

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    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.

    Item Type: Article
    Journal or Publication Title: Physical Review E
    Subjects:
    Departments: Faculty of Science and Technology > Physics
    ID Code: 680
    Deposited By: Dr Henning Schomerus
    Deposited On: 31 Oct 2007
    Refereed?: Yes
    Published?: Published
    Last Modified: 26 Jul 2012 18:18
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/680

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