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

نویسندگان

  • H Schomerus
  • M Titov
چکیده

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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عنوان ژورنال:
  • Physical review. E, Statistical, nonlinear, and soft matter physics

دوره 66 6 Pt 2  شماره 

صفحات  -

تاریخ انتشار 2002