English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present a formalism for obtaining the statistical properties offunctionals and inverse functionals of the paths of a particle diffusing in aone-dimensional quenched random potential. We demonstrate the implementation ofthe formalism in two specific examples: (1) where the functional corresponds tothe local time spent by the particle around the origin and (2) where thefunctional corresponds to the occupation time spent by the particle on thepositive side of the origin, within an observation time window of size $t$. Wecompute the disorder average distributions of the local time, the inverse localtime, the occupation time and the inverse occupation time, and show that inmany cases disorder modifies the behavior drastically.Comment: Revtex two column 27 pages, 10 figures, 3 table

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