Singular probability distribution of shot-noise driven systems

Akihisa Ichiki, Yukihiro Tadokoro, and M. I. Dykman
Phys. Rev. E 87, 012119 – Published 16 January 2013

Abstract

We study the stationary probability distribution of a system driven by shot noise. We find that both in the overdamped and underdamped regime, the coordinate distribution displays power-law singularities in its central part. For sufficiently low rate of noise pulses they correspond to distribution peaks. We find the positions of the peaks and the corresponding exponents. In the underdamped regime the peak positions are given by a geometric progression. The energy distribution in this case also displays multiple peaks with positions given by a geomet-ric progression. Such structure is a signature of the shot-noise induced fluctuations. The analytical results are in excellent agreement with numerical simulations.

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  • Received 8 November 2012

DOI:https://doi.org/10.1103/PhysRevE.87.012119

©2013 American Physical Society

Authors & Affiliations

Akihisa Ichiki1, Yukihiro Tadokoro1, and M. I. Dykman2

  • 1Toyota Central R&D Labs., Inc., Nagakute, Aichi 480-1192, Japan
  • 2Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA

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Issue

Vol. 87, Iss. 1 — January 2013

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