First-passage time distribution of a Brownian particle harmonically confined in a viscoelastic bath
Abstract
We investigate theoretically and experimentally the first passage-time properties of a spherical Brownian particle that is harmonically trapped at thermal equilibrium in a fluid at constant temperature. By using the overdamped version of the generalized Langevin equation, we derive a general expression for the probability density function of the time that the particle takes to reach for the first time the minimum of the potential starting from an arbitrary position. We show that such a first-passage time distribution can be implicitly expressed in terms of the friction memory kernel that encodes the interaction of the particle with its surroundings, and correctly reduces to previously found expressions in the case of a Markovian viscous bath. We validate our theoretical results by measuring the first-passage time of colloidal beads optically trapped in non-Markovian baths such as viscoelastic polymer and micellar solutions, as well as in a viscous glycerol/water mixture and water, which behave as Markovian media, having quantitative agreement with the derived expressions. In particular, we find that the mean first-passage time in a viscoelastic bath can surpass that in a viscous medium of the same zero-shear viscosity due to the emergence of slowly decaying tails in the first-passage time probability density of the former.
Versions
Related
- Absence of hidden analytic conserved quantities in harmonically confined rods
- Distribution Functions and Moments of Harmonically Trapped Inertial Run-and-Tumble Particles in a Shear-Thickening Medium
- Quantitative measurement of fluid inertial effects in confined Brownian motion
- The distribution of the moment of inertia for harmonically trapped noninteracting Bosons at finite temperature: Large deviations
- Linear and nonlinear active microrheology of viscous, viscoelastic, and elastic media: A fluid particle dynamics approach
BibTeX
@misc{ferrer2026firstpassage,
title = {{First-passage time distribution of a Brownian particle harmonically confined in a viscoelastic bath}},
author = {Brandon R. Ferrer and Juan Ruben Gomez-Solano},
howpublished = {arXiv},
year = {2026},
month = may,
doi = {10.48550/arxiv.2605.25215},
eprint = {2605.25215},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.25215},
}
RIS
TY - UNPB
TI - First-passage time distribution of a Brownian particle harmonically confined in a viscoelastic bath
AU - Brandon R. Ferrer
AU - Juan Ruben Gomez-Solano
PY - 2026
DA - 2026/05/24
PB - arXiv
DO - 10.48550/arxiv.2605.25215
UR - https://arxiv.org/abs/2605.25215
AB - We investigate theoretically and experimentally the first passage-time properties of a spherical Brownian particle that is harmonically trapped at thermal equilibrium in a fluid at constant temperature. By using the overdamped version of the generalized Langevin equation, we derive a general expression for the probability density function of the time that the particle takes to reach for the first time the minimum of the potential starting from an arbitrary position. We show that such a first-passage time distribution can be implicitly expressed in terms of the friction memory kernel that encodes the interaction of the particle with its surroundings, and correctly reduces to previously found expressions in the case of a Markovian viscous bath. We validate our theoretical results by measuring the first-passage time of colloidal beads optically trapped in non-Markovian baths such as viscoelastic polymer and micellar solutions, as well as in a viscous glycerol/water mixture and water, which behave as Markovian media, having quantitative agreement with the derived expressions. In particular, we find that the mean first-passage time in a viscoelastic bath can surpass that in a viscous medium of the same zero-shear viscosity due to the emergence of slowly decaying tails in the first-passage time probability density of the former.
ER -