First passage time problems in time-dependent fields

Journal Article · Fri Apr 01 04:00:00 EST 1988 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01015328· OSTI ID:6314332

Fletcher, J E; Havlin, S; Weiss, G H

This paper discusses the simplest first passage time problems for random walks and diffusion processes on a line segment. When a diffusing particle moves in a time-varying field, use of the adjoint equation does not lead to any simplification in the calculation of moments of the first passage time as is the case for diffusion in a time-invariant field. We show that for a discrete random walk in the presence of a sinusoidally varying field there is a resonant frequency omega* for which the mean residence time on the line segment in a minimum. It is shown that for a random walk on a line segment of length L the mean residence time goes like L/sup 2/ for large L when omega omega*, but when omega = omega* the dependence is proportional to L. The results of our simulation are numerical, but can be regarded as exact. Qualitatively similar results are shown to hold for diffusion processes by a perturbation expansion in powers of a dimensionless velocity. These results are extended to higher values of this parameter by a numerical solution of the forward equation.

• Research Organization: National Institutes of Health, Bethesda, MD (USA)
• OSTI ID: 6314332
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 51:1-2; ISSN JSTPB
• Country of Publication: United States
• Language: English

Related Subjects

656002* -- Condensed Matter Physics-- General Techniques in Condensed Matter-- (1987-)
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ABSORPTION
CRYSTAL LATTICES
CRYSTAL STRUCTURE
DIFFUSION
ELECTRIC FIELDS
MATHEMATICAL MODELS
MECHANICS
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
PARTICLE MODELS
PERTURBATION THEORY
RANDOMNESS
STATISTICAL MECHANICS
TIME DEPENDENCE
TRANSPORT THEORY