Memory effects in the asymptotic diffusive behavior of a classical oscillator described by a generalized Langevin equation.
We investigate the memory effects present in the asymptotic dynamics of a classical harmonic oscillator governed by a generalized Langevin equation. Using Laplace analysis together with Tauberian theorems we derive asymptotic expressions for the mean values, variances, and velocity autocorrelation function in terms of the long-time behavior of the memory kernel and the correlation function of the random force. The internal and external noise cases are analyzed. A simple criterion to determine if the diffusion process is normal or anomalous is established.
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Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina. mad@df.uba.ar
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