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Statistics of finite-time Lyapunov exponents in a random time-dependent potential | | H. Schomerus
; M. Titov
; | | Date: |
17 Apr 2002 | | Journal: | Phys. Rev. E 66, 066207 (2002) DOI: 10.1103/PhysRevE.66.066207 | | Subject: | Disordered Systems and Neural Networks; Mesoscopic Systems and Quantum Hall Effect; Chaotic Dynamics | cond-mat.dis-nn cond-mat.mes-hall nlin.CD | | 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_infty) 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 random time-dependent potential how the distribution function P(lambda;t) approaches the limiting distribution P(lambda;infty)=delta(lambda-lambda_infty). Our method also applies to the tail of the distribution, which determines the growth rates of positive moments of M_{ij}. The results are also applicable to the problem of wave-function localization in a disordered one-dimensional potential. | | Source: | arXiv, cond-mat/0204371 | | Other source: | [GID 216734] pmid12513384 | | Services: | Forum | Review | PDF | Favorites | |
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