Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

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