Non-crossing run-and-tumble particles on a line

Abstract

We study active particles performing independent run and tumble motion on an infinite line with velocities $v_0\sigma (t)$, where $\sigma (t)=\pm 1$ is a dichotomous telegraphic noise with constant flipping rate $\gamma$. We first consider one particle in the presence of an absorbing wall at $x=0$ and calculate the probability that it has survived up to time $t$ and is at position $x$ at time $t$. We then consider two particles with independent telegraphic noises and compute exactly the probability that they do not cross up to time $t$. Contrarily to the case of passive (Brownian) particles this two-RTP problem can not be reduced to a single RTP with an absorbing wall. Nevertheless, we are able to compute exactly the probability of no-crossing of two independent RTP's up to time $t$ and find that it decays at large time as $t^{-1/2}$ with an amplitude that depends on the initial condition. The latter allows to define an effective length scale, analogous to the so called `` Milne extrapolation length'' in neutron scattering, which we demonstrate to be a fingerprint of the active dynamics.

arXiv comment19 pages, 3 figures; revised version, Refs. added

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Cited by in corpus (46)

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• Generalised `Arcsine' laws for run-and-tumble particle in one dimension
• Current fluctuations in non-interacting run-and-tumble particles in one-dimension
• 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
• Velocity and diffusion constant of an active particle in a one dimensional force field
• Position distribution in a generalised run and tumble process
• Survival probability of a run-and-tumble particle in the presence of a drift
• Exact position distribution of a harmonically-confined run-and-tumble particle in two dimensions
• Hard core run and tumble particles on a one dimensional lattice
• Mean area of the convex hull of a run and tumble particle in two dimensions
• 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
• Encounter-based model of a run-and-tumble particle II: absorption at sticky boundaries
• Stationary nonequilibrium bound state of a pair of run and tumble particles
• Local time for run and tumble particle
• First-encounter time of two diffusing particles in confinement
• 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
• Extremal statistics of a one dimensional run and tumble particle with an absorbing wall
• Encounter-based model of a run-and-tumble particle
• Current fluctuations in an interacting active lattice gas
• Interacting, running and tumbling: the active Dyson Brownian motion
• Optimal mean first-passage time of a run-and-tumble particle in a class of one-dimensional confining potentials
• Generalized disorder averages and current fluctuations in run and tumble particles
• Smoluchowski flux and Lamb-Lion Problems for Random Walks and Lévy Flights with a Constant Drift
• Order-preserving dynamics in one dimension -- single-file diffusion and caging from the perspective of dynamical density functional theory
• Generating constrained run-and-tumble trajectories
• First passage statistics of active random walks on one and two dimensional lattices
• Dynamical crossovers and correlations in a harmonic chain of active particles
• Large deviations in statistics of the local time and occupation time for a run and tumble particle
• Ergodic theory of multi-layer interacting particle systems
• Run-and-tumble motion: the role of reversibility
• Non-equilibrium phase transitions in active rank diffusions
• Crossover dynamics and non-Gaussian fluctuations in inertial active chains
• The one-dimensional telegraphic process with noninstantaneous stochastic resetting
• Run-and-tumble particles on a line with a fertile site
• Trapping of a run-and-tumble particle in an inhomogeneous domain: the weak noise limit
• Boundary layers, transport and universal distribution in boundary driven active systems