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

The paper addresses Brownian motion in the logarithmic potential withtime-dependent strength, $U(x,t) = g(t) \log(x)$, subject to the absorbingboundary at the origin of coordinates. Such model can represent kinetics ofdiffusion-controlled reactions of charged molecules or escape of Brownianparticles over a time-dependent entropic barrier at the end of a biologicalpore. We present a simple asymptotic theory which yields the long-time behaviorof both the survival probability (first-passage properties) and the moments ofthe particle position (dynamics). The asymptotic survival probability, i.e.,the probability that the particle will not hit the origin before a given time,is a functional of the potential strength. As such it exhibits a rather variedbehavior for different functions $g(t)$. The latter can be grouped into threeclasses according to the regime of the asymptotic decay of the survivalprobability. We distinguish 1. the regular (power-law decay), 2. the marginal(power law times a slow function of time), and 3. the regime of enhancedabsorption (decay faster than the power law, e.g., exponential). Results of theasymptotic theory show good agreement with numerical simulations.

Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties