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