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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10318376" target="_blank" >RIV/00216208:11320/15:10318376 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1063/1.4931474" target="_blank" >http://dx.doi.org/10.1063/1.4931474</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4931474" target="_blank" >10.1063/1.4931474</a>

Result language
angličtina
Original language name
Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties
Original language description
The paper addresses Brownian motion in the logarithmic potential with time-dependent strength, U(x, t) = g(t) log(x), subject to the absorbing boundary at the origin of coordinates. Such model can represent kinetics of diffusion-controlled reactions of charged molecules or escape of Brownian particles over a time-dependent entropic barrier at the end of a biological pore. We present a simple asymptotic theory which yields the long-time behavior of both the survival probability (first-passage properties)and the moments of the 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 varied behavior for different functions g(t). The latter can be grouped into three classes according to the regime of the asymptotic decay of the survival probability. We distinguish 1. the regular (power-law decay), 2. the marginal (power law
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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