A Paradox in the Langevin Equation with Long-Time Noise Correlations

Details A Paradox in the Langevin Equation with Long-Time Noise Correlations A Paradox in the Langevin Equation with Long-Time Noise Correlations

1999-12-22

arxiv.org/abs/cond-mat/9912407v1

Physics

Condensed Matter

Statistical Mechanics

10 pages + 2 Figures, RevTeX

Scientific paper

We solve the generalized Langevin equation driven by a stochastic force with power-law autocorrelation function. A stationary Markov process has been applied as a model of the noise. However, the resulting velocity variance does not stabilizes but diminishes with time. It is shown that algebraic distributions can induce such non-stationary affects. Results are compared to those obtained with a deterministic random force. Consequences for the diffusion process are also discussed.

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