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

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Statistics of finite-time Lyapunov exponents in a random time-dependent potential. / Schomerus, H.; Titov, M.
In: Physical Review E, Vol. 66, 2002, p. 066207.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Schomerus, H. ; Titov, M. / Statistics of finite-time Lyapunov exponents in a random time-dependent potential. In: Physical Review E. 2002 ; Vol. 66. pp. 066207.

Bibtex

@article{c0fd4571c2724c8d98b0f686962f5b42,
title = "Statistics of finite-time Lyapunov exponents in a random time-dependent potential.",
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 {\^I}», obtained from the elements Mij of the stability matrix M. For globally chaotic dynamics, {\^I}» tends to a unique value (the usual Lyapunov exponent {\^I}»{\^a}��) 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({\^I}»;t) approaches the limiting distribution P({\^I}»;{\^a}��)={\^I}´({\^I}»-{\^I}»{\^a}��). 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.",
author = "H. Schomerus and M. Titov",
year = "2002",
language = "English",
volume = "66",
pages = "066207",
journal = "Physical Review E",
issn = "1550-2376",
publisher = "American Physical Society",

}

RIS

TY - JOUR

T1 - Statistics of finite-time Lyapunov exponents in a random time-dependent potential.

AU - Schomerus, H.

AU - Titov, M.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

M3 - Journal article

VL - 66

SP - 066207

JO - Physical Review E

JF - Physical Review E

SN - 1550-2376

ER -