title: Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties.
abstract: 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 times a slow function of time), and 3. the regime of enhanced absorption (decay faster than the power law, e.g., exponential). Results of the asymptotic theory show good agreement with numerical simulations.
authors.affiliation: Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic.
authors.forename: Artem
authors.initials: A
authors.lastname: Ryabov
authors.affiliation: Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic.
authors.forename: Ekaterina
authors.initials: E
authors.lastname: Berestneva
authors.affiliation: Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic.
authors.forename: Viktor
authors.initials: V
authors.lastname: Holubec
mesh_terms: D003198:Computer Simulation; D019277:Entropy; D007700:Kinetics; D008956:Models, Chemical; D009038:Motion; D011336:Probability; D013997:Time Factors