Run-and-tumble particle in one-dimensional potentials: mean first-passage time and applications

Abstract

We study a one-dimensional run-and-tumble particle (RTP), which is a prototypical model for active system, moving within an arbitrary external potential. Using backward Fokker-Planck equations, we derive the differential equation satisfied by its mean first-passage time (MFPT) to an absorbing target, which, without any loss of generality, is placed at the origin. Depending on the shape of the potential, we identify four distinct ``phases'', with a corresponding expression for the MFPT in every case, which we derive explicitly. To illustrate these general expressions, we derive explicit formulae for two specific cases which we study in detail: a double-well potential and a logarithmic potential. We then present different applications of these general formulae to (i) the generalization of the Kramer's escape law for an RTP in the presence of a potential barrier, (ii) the ``trapping'' time of an RTP moving in a harmonic well and (iii) characterizing the efficiency of the optimal search strategy of an RTP subjected to stochastic resetting. Our results reveal that the MFPT of an RTP in an external potential exhibits a far more complex and, at times, counter-intuitive behavior compared to that of a passive particle (e.g., Brownian) in the same potential.

34 pages, 16 figures

References in corpus (44)

• Active Particles in Complex and Crowded Environments
• Active Brownian Particles. From Individual to Collective Stochastic Dynamics
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Diffusion with Stochastic Resetting
• Stochastic Resetting and Applications
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Diffusive transport without detailed balance in motile bacteria: Does microbiology need statistical physics?
• Diffusion with Optimal Resetting
• Active matter
• Self-propulsion of a catalytically active particle near a planar wall: from reflection to sliding and hovering
• The statistical physics of active matter: from self-catalytic colloids to living cells
• Run and tumble particle under resetting: a renewal approach
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Run-and-tumble particle in one-dimensional confining potential: Steady state, relaxation and first passage properties
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
• Activated escape of a self-propelled particle from a metastable state
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• Optimizing persistent random searches
• Active particles under confinement: Aggregation at the wall and gradient formation inside a channel
• Escape rate of active particles in the effective equilibrium approach
• Confined run-and-tumble swimmers in one dimension
• Stationary superstatistics distributions of trapped run-and-tumble particles
• Escape dynamics of active particles in multistable potentials
• Active Brownian particles near straight or curved walls: Pressure and boundary layers
• Characterization and Control of the Run-and-Tumble Dynamics of {\it Escherichia Coli}
• Nonlocal stationary probability distributions and escape rates for an active Ornstein-Uhlenbeck particle
• Optimal search strategies of run-and-tumble walks
• Dynamics and escape of active particles in a harmonic trap
• Kramers escape of a self-propelled particle
• Velocity and diffusion constant of an active particle in a one dimensional force field
• Pressure and Flow of Exponentially Self-Correlated Active Particles
• Survival probability of a run-and-tumble particle in the presence of a drift
• Time to reach the maximum for a stationary stochastic process
• Nonequilibirum steady state for harmonically-confined active particles
• Run-and-Tumble particle in inhomogeneous media in one dimension
• Encounter-based model of a run-and-tumble particle II: absorption at sticky boundaries
• Ramifications of disorder on active particles in one dimension
• Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates
• Freezing transition in the barrier crossing rate of a diffusing particle
• Extremal statistics of a one dimensional run and tumble particle with an absorbing wall
• Optimal mean first-passage time of a run-and-tumble particle in a class of one-dimensional confining potentials
• Relating absorbing and hard wall boundary conditions for a one-dimensional run-and-tumble particle
• Asymptotic analysis and simulation of mean first passage time for active Brownian particles in 1-D
• Survival probability and position distribution of a run and tumble particle in $U(x)=\alpha |x|$ potential with an absorbing boundary

Cited by in corpus (4)

• Martingale approach for first-passage problems of time-additive observables in Markov processes
• Nonequilibrium steady state of Brownian motion in an intermittent potential
• Run-and-tumble exact work statistics in a lazy quantum measurement engine: stochastic information processing
• Local entropy production rate of run-and-tumble particles