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

Schomerus, H., & Titov, M. (2002). Statistics of finite-time Lyapunov exponents in a random time- dependent potential. Physical Review E, 66(6): 066207. Retrieved from http://ojps.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLEEE8000066000006066207000001&idtype=cvips&gifs=yes.

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 Creators:
Schomerus, H.1, Author              
Titov, M.1, Author              
Affiliations:
1Max Planck Institute for the Physics of Complex Systems, Max Planck Society, ou_2117288              

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 MPIPKS: Time dependent processes
 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 lambda, obtained from the elements M-ij of the stability matrix M. For globally chaotic dynamics, lambda tends to a unique value (the usual Lyapunov exponent lambda(infinity)) 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(lambda;t) approaches the limiting distribution P(lambda;infinity) = delta(lambda- lambda(infinity)). Our method also applies to the tail of the distribution, which determines the growth rates of moments of M-ij. The results are also applicable to the problem of wave- function localization in a disordered one-dimensional potential.

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Language(s): eng - English
 Dates: 2002-12
 Publication Status: Published in print
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 Rev. Type: Peer
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Title: Physical Review E
  Alternative Title : Phys. Rev. E
Source Genre: Journal
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Pages: - Volume / Issue: 66 (6) Sequence Number: 066207 Start / End Page: - Identifier: ISSN: 1063-651X