On exact time-averages of a massive Poisson particle

Details On exact time-averages of a massive Poisson particle On exact time-averages of a massive Poisson particle

2011-05-19

arxiv.org/abs/1105.3877v1

J. Stat. Mech. (2011) P06010

Physics

Condensed Matter

Statistical Mechanics

21 pages, 5 figures. To be published in Journal of Statistical Mechanics: Theory and Experiment

Scientific paper

10.1088/1742-5468/2011/06/P06010

In this work we study, under the Stratonovich definition, the problem of the damped oscillatory massive particle subject to a heterogeneous Poisson noise characterised by a rate of events, \lambda (t), and a magnitude, \Phi, following an exponential distribution. We tackle the problem by performing exact time-averages over the noise in a similar way to previous works analysing the problem of the Brownian particle. From this procedure we obtain the long-term equilibrium distributions of position and velocity as well as analytical asymptotic expressions for the injection and dissipation of energy terms. Considerations on the emergence of stochastic resonance in this type of system are also set forth.

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