Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap

Abstract

We study the motion of a one-dimensional run-and-tumble particle with three discrete internal states in the presence of a harmonic trap of stiffness $\mu .$ The three internal states, corresponding to positive, negative and zero velocities respectively, evolve following a jump process with rate $\gamma$. We compute the stationary position distribution exactly for arbitrary values of $\mu$ and $\gamma$ which turns out to have a finite support on the real line. We show that the distribution undergoes a shape-transition as $\beta =\gamma /\mu$ is changed. For $\beta <1,$ the distribution has a double-concave shape and shows algebraic divergences with an exponent $(\beta -1)$ both at the origin and at the boundaries. For $\beta >1,$ the position distribution becomes convex, vanishing at the boundaries and with a single, finite, peak at the origin. We also show that for the special case $\beta =1,$ the distribution shows a logarithmic divergence near the origin while saturating to a constant value at the boundaries.

13 pages, 2 figures

References in corpus (10)

• Novel type of phase transition in a system of self-driven particles
• Hydrodynamic attraction of swimming microorganisms by surfaces
• Diffusive transport without detailed balance in motile bacteria: Does microbiology need statistical physics?
• Active matter
• Activity-induced phase separation and self-assembly in mixtures of active and passive particles
• Sedimentation, trapping, and rectification of dilute bacteria
• Gravitaxis of asymmetric self-propelled colloidal particles
• Intermediate scattering function of an anisotropic active Brownian particle
• Exact Solution of Two Interacting Run-and-Tumble Random Walkers with Finite Tumble Duration
• Active Brownian Particles Escaping a Channel in Single File

Cited by in corpus (48)

• Time-(ir)reversibility in active matter: from micro to macro
• Universal survival probability for a $d$-dimensional run-and-tumble particle
• Run-and-tumble motion: field theory and entropy production
• Universal Properties of a Run-and-Tumble Particle in Arbitrary Dimension
• 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
• AOUP in the presence of Brownian noise: a perturbative approach
• Exact position distribution of a harmonically-confined run-and-tumble particle in two dimensions
• Mean area of the convex hull of a run and tumble particle in two dimensions
• Hard core run and tumble particles on a one dimensional lattice
• 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
• Inclusions, Boundaries and Disorder in Scalar Active Matter
• Run-and-Tumble particle in inhomogeneous media in one dimension
• Calorimetry for active systems
• Heat fluctuations in a harmonic chain of active particles
• Local time for run and tumble particle
• Stationary nonequilibrium bound state of a pair of run and tumble particles
• Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates
• Positing the problem of stationary distributions of active particles as third-order differential equation
• Brownian particle in a Poisson-shot-noise active bath: exact statistics, effective temperature, and inference
• Extremal statistics of a one dimensional run and tumble particle with an absorbing wall
• 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
• Exactly solvable model of a passive Brownian heat engine and its comparison with active engines
• Generating constrained run-and-tumble trajectories
• Exact solution of a boundary tumbling particle system in one dimension
• Noninteracting particles in a harmonic trap with a stochastically driven center
• Dynamical crossovers and correlations in a harmonic chain of active particles
• Statistical mechanics of passive Brownian particles in a fluctuating harmonic trap
• Stationary distributions of propelled particles as a system with quenched disorder
• Optimal run-and-tumble in slit-like confinement
• Inducing a bound state between active particles
• Tagged particle behavior in a harmonic chain of direction reversing active Brownian particles
• Local detailed balance for active particle models
• Run-and-tumble motion in trapping environments
• Kuramoto model with run-and-tumble dynamics
• Run-and-tumble particles in slit geometry as a splitting probability problem
• Tracer dynamics in the active random average process
• Orthogonal run-and-tumble walks
• Long time behavior of run-and-tumble particles in two dimensions
• Run-and-tumble particles on a line with a fertile site
• Crystal to liquid cross-over for active particles with inverse-square power-law interaction
• Trapping of a run-and-tumble particle in an inhomogeneous domain: the weak noise limit
• Universal framework for the long-time position distribution of free active particles
• First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension