Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

Details Lyapunov exponent of the random frequency oscillator: cumulant expansion approach Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

2010-08-27

arxiv.org/abs/1008.4708v1

Physics

Condensed Matter

Statistical Mechanics

6 pages, 4 figures, to appear in J. Phys. Conf. Series - LAWNP09

Scientific paper

We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, $\lambda$ and $\lambda^\star$ respectively. We discuss the numerical difficulties that arise in the numerical calculation of $\lambda^\star$ in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically $\lambda^\star$ by using a cumulant expansion including up to the fourth order. Connections with the problem of finding an analytical estimate for the largest Lyapunov exponent of a many-body system with smooth interactions are discussed.

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