Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-01-19
Phys. Rev. E 73, 051102 (2006)
Physics
Condensed Matter
Statistical Mechanics
Revtex two column 27 pages, 10 figures, 3 tables
Scientific paper
10.1103/PhysRevE.73.051102
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.
Comtet Alain
Majumdar Satya N.
Sabhapandit Sanjib
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