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

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Schomerus,  H.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Titov,  M.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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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.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002B-3694-7
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.