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Statistical properties of functionals of the paths of a particle diffusing in a one-dimensional random potential

Sanjib Sabhapandit1,2, Satya N. Majumdar1, and Alain Comtet1,2

  • 1Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, Bâtiment 100, 91405 Orsay Cedex, France
  • 2Université Pierre et Marie Curie, Paris 6, Institut Henri Poincaré, 11 rue Pierre et Marie Curie, Paris, F-75005, France

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Phys. Rev. E 73, 051102 – Published 1 May, 2006

DOI: https://doi.org/10.1103/PhysRevE.73.051102

Abstract

We present a formalism for obtaining the statistical properties of functionals and inverse functionals of the paths of a particle diffusing in a one-dimensional quenched random potential. We demonstrate the implementation of the formalism in two specific examples: (1) where the functional corresponds to the local time spent by the particle around the origin and (2) where the functional corresponds to the occupation time spent by the particle on the positive side of the origin, within an observation time window of size t. We compute the disorder average distributions of the local time, the inverse local time, the occupation time, and the inverse occupation time and show that in many cases disorder modifies the behavior drastically.

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Phys. Rev. E 73, 051102– Published 1 May, 2006
  • Received 19 January 2006

© 2006 American Physical Society

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