Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point

Details Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point

2008-08-15

arxiv.org/abs/0808.2207v3

J. Phys. A: Math. Theor. 42 (2009) 165002

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1088/1751-8113/42/16/165002

A parametric oscillator with damping driven by white noise is studied. The mean square displacement (MSD) in the long-time limit is derived analytically for the case that the static force vanishes, which was not treated in the past work \cite{tashiro07}. The formula is asymptotic but is applicable to a general periodic function. On the basis of this formula, some periodic functions reducing MSD remarkably are proposed.

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