Threshold-crossing statistics in diffusion with a time-dependent control parameter

Details Threshold-crossing statistics in diffusion with a time-dependent control parameter Threshold-crossing statistics in diffusion with a time-dependent control parameter

Nov 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006smpr.confe..17b&link_type=abstract

Proceedings of the International conference on Statistical Mechanics of Plasticity and Related Instabilities. August 29-Septembe

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

We study two important aspects of the diffusion of a free particle in the presence of a time- dependent control parameter. The latter is represented by a friction coefficient that is a given function of time. We solve the stochastic Liouville equation (the Fokker-Planck equation) for the probability density of the particle in phase space, i. e., in both position and velocity. The exact solution is then used to analyze the behavior of (i) the variance in the position, a global charac- terizer of the system; and (ii) the mean rate of crossings of an arbitrary threshold in the position, a local characterizer. The former is the more conventional descriptor of diffusive processes, but the latter provides valuable complementary information on the dynamical behavior. Depending on the long-time behavior of the friction coefficient, the asymptotic behaviors of both these char- acterizers vary, and exhibit several cross-overs. This helps elucidate the nature of the interplay between the destabilizing effects of the noise and the stabilizing tendency of the damping, as the latter undergoes a controlled variation in time.

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