First Exit Times of Harmonically Trapped Particles: A Didactic Review

We revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by one- or multi-dimensional Ornstein-Uhlenbeck process. We start by recalling the main derivation steps of a propagator using Langevin and Fokker-Planck equations. The mea...

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Veröffentlicht in:arXiv.org
1. Verfasser: Grebenkov, D S
Format: Paper
Sprache:Englisch
Veröffentlicht: Ithaca Cornell University Library, arXiv.org 22.06.2025
Schlagworte:
Adhesive bonding
Brownian motion
Eigenvalues
Eigenvectors
Hypergeometric functions
Mathematical analysis
Mechanical properties
Numerical analysis
Operators (mathematics)
Ornstein-Uhlenbeck process
Particle tracking
Proteins
Trapped particles
ISSN:2331-8422
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Zusammenfassung:We revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by one- or multi-dimensional Ornstein-Uhlenbeck process. We start by recalling the main derivation steps of a propagator using Langevin and Fokker-Planck equations. The mean exit time, the moment-generating function, and the survival probability are then expressed through confluent hypergeometric functions and thoroughly analyzed. We also present a rapidly converging series representation of confluent hypergeometric functions that is particularly well suited for numerical computation of eigenvalues and eigenfunctions of the governing Fokker-Planck operator. We discuss several applications of first exit times such as detection of time intervals during which motor proteins exert a constant force onto a tracer in optical tweezers single-particle tracking experiments; adhesion bond dissociation under mechanical stress; characterization of active periods of trend following and mean-reverting strategies in algorithmic trading on stock markets; relation to the distribution of first crossing times of a moving boundary by Brownian motion. Some extensions are described, including diffusion under quadratic double-well potential and anomalous diffusion.
Bibliographie:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1411.3598