Motion of a Brownian molecule in the presence of reactive boundaries

Abstract

We study the one-dimensional motion of a Brownian particle inside a confinement described by two reactive boundaries which can partially reflect or absorb the particle. Understanding the effects of such boundaries is important in physics, chemistry and biology. We compute the probability density of the particle displacement exactly, from which we derive expressions for the survival probability and the mean absorption time as a function of the reactive coefficients. Furthermore, using the Feynman-Kac formalism, we investigate the reaction time profile, which is the fluctuating time spent by the particle at a given location, both till a fixed observation time and till the absorption time. Our analytical results are compared to numerical simulations showing perfect agreement.

30 pages, 7 figures

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Cited by in corpus (13)

• Dynamical large deviations of reflected diffusions
• First-passage Brownian functionals with stochastic resetting
• Resetting transition is governed by an interplay between thermal and potential energy
• Microscopic Theory of Adsorption Kinetics
• First hitting times to intermittent targets
• Local time for run and tumble particle
• First-passage functionals for Ornstein Uhlenbeck process with stochastic resetting
• Extremal statistics of a one dimensional run and tumble particle with an absorbing wall
• Escape of a Sticky Particle
• Gated reactions in discrete time and space
• Local time of an Ornstein-Uhlenbeck particle
• Subdiffusion in a system with a partially permeable partially absorbing wall
• Non-standard diffusion under Markovian resetting in bounded domains