Run-and-tumble particle in one-dimensional confining potential: Steady state, relaxation and first passage properties

Abstract

We study the dynamics of a one-dimensional run and tumble particle subjected to confining potentials of the type $V(x)=\alpha |x{|}^p$, with $p>0$. The noise that drives the particle dynamics is telegraphic and alternates between $\pm 1$ values. We show that the stationary probability density $P(x)$ has a rich behavior in the $(p,\alpha )$-plane. For $p>1$, the distribution has a finite support in $[x_{-},x_{+}]$ and there is a critical line ${\alpha }_c(p)$ that separates an active-like phase for $\alpha >{\alpha }_c(p)$ where $P(x)$ diverges at $x_{\pm }$, from a passive-like phase for $\alpha <{\alpha }_c(p)$ where $P(x)$ vanishes at $x_{\pm }$. For $p<1$, the stationary density $P(x)$ collapses to a delta function at the origin, $P(x)=\delta (x)$. In the marginal case $p=1$, we show that, for $\alpha <{\alpha }_c$, the stationary density $P(x)$ is a symmetric exponential, while for $\alpha >{\alpha }_c$, it again is a delta function $P(x)=\delta (x)$. For the special cases $p=2$ and $p=1$, we obtain exactly the full time-dependent distribution $P(x,t)$, that allows us to study how the system relaxes to its stationary state. In addition, in these two cases, we also study analytically the full distribution of the first-passage time to the origin. Numerical simulations are in complete agreement with our analytical predictions.

15 pages, 12 figures. Published version

References in corpus (4)

• Motility-Induced Phase Separation
• Run and tumble particle under resetting: a renewal approach
• Dynamics of a self-propelled particle in a harmonic trap
• Stationary superstatistics distributions of trapped run-and-tumble particles

Cited by in corpus (135)

• Time-(ir)reversibility in active matter: from micro to macro
• Activated escape of a self-propelled particle from a metastable state
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• Steady State of an Active Brownian Particle in Two-Dimensional Harmonic Trap
• Run-and-tumble particles in two-dimensions : Marginal position distributions
• A First-Order Dynamical Transition in the displacement distribution of a Driven Run-and-Tumble Particle
• Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap
• Long time position distribution of an active Brownian particle in two dimensions
• Run-and-Tumble particles in Two-dimensions under Stochastic Resetting
• Optical cold damping of neutral nanoparticles near the ground state in an optical lattice
• Active Brownian Motion in two-dimensions under Stochastic Resetting
• Generalised `Arcsine' laws for run-and-tumble particle in one dimension
• Fluctuating motion in an active environment
• Non-crossing run-and-tumble particles on a line
• Run-and-tumble motion: field theory and entropy production
• Current fluctuations in non-interacting run-and-tumble particles in one-dimension
• The convex hull of the run-and-tumble particle in a plane
• The active trap model
• Active Brownian Motion with Directional Reversals
• Condensation transition in the late-time position of a Run-and-Tumble particle
• Universal Properties of a Run-and-Tumble Particle in Arbitrary Dimension
• Occupation time of a run-and-tumble particle with resetting
• Distribution of the time of the maximum for stationary processes
• Velocity and diffusion constant of an active particle in a one dimensional force field
• Universal scaling in active single-file dynamics
• Recoil-limited feedback cooling of single nanoparticles near the ground state in an optical lattice
• Position distribution in a generalised run and tumble process
• Translational and rotational dynamics of a self-propelled Janus probe in crowded environments
• Active Brownian particle in harmonic trap: exact computation of moments, and re-entrant transition
• Second law for active heat engines
• Survival probability of a run-and-tumble particle in the presence of a drift
• Direction reversing active Brownian particle in a harmonic potential
• Universal tradeoff relation between speed, uncertainty, and dissipation in nonequilibrium stationary states
• Mean area of the convex hull of a run and tumble particle in two dimensions
• Time to reach the maximum for a stationary stochastic process
• Exact position distribution of a harmonically-confined run-and-tumble particle in two dimensions
• Active Brownian particles: mapping to equilibrium polymers and exact computation of moments
• Hard core run and tumble particles on a one dimensional lattice
• Tracer dynamics in one dimensional gases of active or passive particles
• Nonequilibirum steady state for harmonically-confined active particles
• Run-and-tumble motion in a linear ratchet potential: Analytic solution, power extraction, and first-passage properties
• Run-and-Tumble particle in inhomogeneous media in one dimension
• Calorimetry for active systems
• Encounter-based model of a run-and-tumble particle II: absorption at sticky boundaries
• Local time for run and tumble particle
• Stationary nonequilibrium bound state of a pair of run and tumble particles
• Ramifications of disorder on active particles in one dimension
• Modelling Active Non-Markovian Oscillations
• Universal survival probability for a correlated random walk and applications to records
• Gap statistics of two interacting run and tumble particles in one dimension
• Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates
• Control of Active Brownian Particles: An exact solution
• Fluctuations of entropy production of a run-and-tumble particle
• Positing the problem of stationary distributions of active particles as third-order differential equation
• Active Brownian Particles in a Circular Disk with an Absorbing Boundary
• Current fluctuations in stochastically resetting particle systems
• Field Theory of Free Run and Tumble Particles in d Dimensions
• Attractor-driven matter
• Extremal statistics of a one dimensional run and tumble particle with an absorbing wall
• Encounter-based model of a run-and-tumble particle
• Switching interacting particle systems: scaling limits, uphill diffusion and boundary layer
• First passage time distribution of active thermal particles in potentials
• Spectral density of individual trajectories of an active Brownian particle
• Active Brownian motion with speed fluctuations in arbitrary dimensions: exact calculation of moments and dynamical crossovers
• Interacting, running and tumbling: the active Dyson Brownian motion
• Entropy production of active particles in underdamped regime
• A comparison of dynamical fluctuations of biased diffusion and run-and-tumble dynamics in one dimension
• First hitting times between a run-and-tumble particle and a stochastically-gated target
• Optimal mean first-passage time of a run-and-tumble particle in a class of one-dimensional confining potentials
• Active Random Walks in One and Two Dimensions
• Nonequilibrium steady state of trapped active particles
• Relating absorbing and hard wall boundary conditions for a one-dimensional run-and-tumble particle
• Work Fluctuations in the Active Ornstein- Uhlenbeck Particle model
• Run-and-tumble particle in one-dimensional potentials: mean first-passage time and applications
• Active noise-driven particles under space-dependent friction in one dimension
• Generating constrained run-and-tumble trajectories
• Self-propulsion with speed and orientation fluctuation: exact computation of moments and dynamical bistabilities in displacement
• Microscopic thermal machines using run-and-tumble particles
• Noninteracting particles in a harmonic trap with a stochastically driven center
• Exact solution of a boundary tumbling particle system in one dimension
• Last-passage time for linear diffusions and application to the emptying time of a box
• Confined run and tumble particles with non-Markovian tumbling statistics
• Age representation of Levy walks: partial density waves, relaxation and first passage time statistics
• Statistical mechanics of passive Brownian particles in a fluctuating harmonic trap
• Pushing run-and-tumble particles through a rugged channel
• Dynamical crossovers and correlations in a harmonic chain of active particles
• Chiral run-and-tumble walker: transport and optimizing search
• Harmonically trapped inertial run-and-tumble particle in one dimension
• Inertial Dynamics of Run-and-Tumble Particle
• Stationary distributions of propelled particles as a system with quenched disorder
• Fluctuations in the active Dyson Brownian motion and the overdamped Calogero-Moser model
• Level crossing statistics in a biologically motivated model of a long dynamic protrusion: passage times, random and extreme excursions
• Ergodic theory of multi-layer interacting particle systems
• Active particle in a harmonic trap driven by a resetting noise: an approach via Kesten variables
• Large deviations in statistics of the convex hull of passive and active particles: A theoretical study
• Local time of an Ornstein-Uhlenbeck particle
• Passive objects in confined active fluids: a localization transition
• Active velocity processes with suprathermal stationary distributions and long-time tails
• Tagged particle behavior in a harmonic chain of direction reversing active Brownian particles
• Optimal run-and-tumble in slit-like confinement
• Inducing a bound state between active particles
• Survival probability and position distribution of a run and tumble particle in $U(x)=\alpha |x|$ potential with an absorbing boundary
• Siegmund duality for physicists: a bridge between spatial and first-passage properties of continuous and discrete time stochastic processes
• Active Brownian particle under stochastic position and orientation resetting in a harmonic trap
• Heat flux direction controlled by power-law oscillators under non-Gaussian fluctuations
• Relaxation to steady states of a binary liquid mixture around an optically heated colloid
• Run-and-tumble motion in trapping environments
• Kuramoto model with run-and-tumble dynamics
• Run-and-tumble motion: the role of reversibility
• Coupling an elastic string to an active bath: the emergence of inverse damping
• Series representations for the characteristic function of the multidimensional Markov random flight
• Splitting probabilities for dynamics in corrugated channels: passive VS active Brownian motion
• Non-equilibrium phase transitions in active rank diffusions
• Tracer dynamics in the active random average process
• Long time behavior of run-and-tumble particles in two dimensions
• Target search by active particles
• Run-and-tumble particles in slit geometry as a splitting probability problem
• Approaching the perfect diode limit through a nonlinear interface
• Local entropy production rate of run-and-tumble particles
• Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Transition-Path Times, Survival Probability, and First-Passage Time
• Dynamical metastability and re-entrant localization of trapped active elements with speed and orientation fluctuations
• Structural fluctuations in active glasses
• Crystal to liquid cross-over for active particles with inverse-square power-law interaction
• Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Finite Rectangular Domain with Absorbing Boundary Conditions
• Work, entropy production, and thermodynamics of information under protocol constraints
• Correlated escape of active particles across a potential barrier
• First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension
• Memory-aware feedback enhances power in active information engines
• A Rayleigh criterion for mechanical instability: inducing activity by chemo-mechanical coupling
• Fluctuations in first passage times and utility of resetting protocol in biochemical systems with two-state toggling
• Mean first passage times of higher-dimensional velocity jump processes
• Universal framework for the long-time position distribution of free active particles
• Boundary layers, transport and universal distribution in boundary driven active systems
• Run-and-tumble particle with saturating rates
• Inverse Clausius Thermodynamics in Run-and-Tumble Dynamics