Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

Abstract

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.

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

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