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Run-and-tumble particle in one-dimensional potentials: Mean first-passage time and applications
Mathis Guéneau1, Satya N Majumdar2, Grégory Schehr1
1Laboratoire de Physique Théorique et Hautes Energies, Sorbonne Université, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France.
Physical Review. E
|February 20, 2025
Summary
This study analyzes the mean first-passage time (MFPT) of a run-and-tumble particle (RTP) in external potentials. The research reveals complex and counterintuitive behaviors compared to passive particles.
Area of Science:
- Statistical Mechanics
- Soft Matter Physics
- Non-equilibrium Systems
Background:
- The run-and-tumble particle (RTP) is a fundamental model for active matter systems.
- Understanding particle dynamics in external potentials is crucial for various physical phenomena.
Purpose of the Study:
- Derive and analyze the mean first-passage time (MFPT) of a 1D RTP in an arbitrary external potential.
- Identify distinct dynamical phases and their corresponding MFPT expressions.
- Explore applications including generalized Kramers escape, trapping times, and optimal search strategies.
Main Methods:
- Utilized backward Fokker-Planck equations to derive the differential equation for MFPT.
- Identified four distinct dynamical phases based on potential landscape.
- Derived explicit MFPT formulas for general potentials and specific cases (double-well, logarithmic).
Main Results:
- Derived general expressions for MFPT in different potential-defined phases.
- Obtained explicit formulas for double-well and logarithmic potentials.
- Demonstrated complex and counterintuitive MFPT behavior compared to Brownian motion.
Conclusions:
- The MFPT of an RTP in external potentials exhibits significantly more complex dynamics than passive particles.
- The derived framework provides a generalized understanding of escape and trapping phenomena for active particles.
- Results offer insights into active matter behavior and optimization of search strategies.
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