First Exit Times of Harmonically Trapped Particles: A Didactic Review
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2014
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| _version_ | 1866918066824151040 |
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| author | Grebenkov, D. S. |
| author_facet | Grebenkov, D. S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1411_3598 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | First Exit Times of Harmonically Trapped Particles: A Didactic Review Grebenkov, D. S. Mathematical Physics Statistical Mechanics 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. |
| title | First Exit Times of Harmonically Trapped Particles: A Didactic Review |
| topic | Mathematical Physics Statistical Mechanics |
| url | https://arxiv.org/abs/1411.3598 |