Gap statistics of two interacting run and tumble particles in one dimension

Abstract

We study the dynamics of the separation (gap) between a pair of interacting run and tumble particles (RTPs) moving in one dimension in the presence of additional thermal noise. On a ring geometry the distribution of the gap approaches a steady state. We analytically compute this distribution and find that this is exponentially localised in space, in contrast to the `jammed' configuration, seen earlier in the absence of thermal noise. We also study the relaxation which is an exponential, characterised by a time scale ${\tau }_r$. We observe that this time scale undergoes a crossover from a size independent value to a size dependent form with increasing size $l$ of the ring. We study the full eigenvalue spectrum of the evolution operator $\mathcal{L}$ and find that the spectrum can be classified into four sectors depending on the symmetries of $\mathcal{L}$. For large $l$, we find explicit expressions for the low lying eigenvalues in each of the sectors. On infinite line the separation does not reach a steady state. In the long times we find that the particles behave as interacting Brownian particles, except for the presence of a peak in the distribution at small separation which is a remnant of activity.

arXiv comment29 pages, 9 figures

References in corpus (36)

• Novel type of phase transition in a system of self-driven particles
• Active Particles in Complex and Crowded Environments
• Motility-Induced Phase Separation
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Long-lived Giant Number Fluctuations in a Swarming Granular Nematic
• Pressure is not a state function for generic active fluids
• Active matter
• Activity-induced phase separation and self-assembly in mixtures of active and passive particles
• Phase separation and rotor self-assembly in active particle suspensions
• A self-propelled particle in an external potential: is there an effective temperature?
• Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Dynamics of a self-propelled particle in a harmonic trap
• Run-and-tumble particle in one-dimensional confining potential: Steady state, relaxation and first passage properties
• Tunable long range forces mediated by self-propelled colloidal hard spheres
• Clustering of microswimmers: Interplay of shape and hydrodynamics
• Active Brownian Motion in Two Dimensions
• Spontaneous flow states in active nematics: a unified picture
• Clustering and heterogeneous dynamics in a kinetic Monte-Carlo model of self-propelled hard disks
• Mesoscopic theory for fluctuating active nematics
• Casimir Effect in Active Matter Systems
• Jamming and Attraction of Interacting Run-and-Tumble Random Walkers
• Mean-field limit for the stochastic Vicsek model
• Phase separation in binary mixtures of active and passive particles
• Exact Hydrodynamic Description of Active Lattice Gases
• Dynamics and density distribution of strongly confined noninteracting nonaligning self-propelled particles in a nonconvex boundary
• Long time position distribution of an active Brownian particle in two dimensions
• Non-crossing run-and-tumble particles on a line
• Active Brownian particles near straight or curved walls: Pressure and boundary layers
• Exact Solution of Two Interacting Run-and-Tumble Random Walkers with Finite Tumble Duration
• Exact spectral solution of two interacting run-and-tumble particles on a ring lattice
• Microscopic derivation of the hydrodynamics of active-Brownian-particle suspensions
• Active Brownian particles: mapping to equilibrium polymers and exact computation of moments
• Ordering dynamics of self-propelled particles in an inhomogeneous medium
• Hydrodynamics, superfluidity and giant number fluctuations in a model of self-propelled particles
• Order-disorder transition in active nematic: A lattice model study

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• From a microscopic solution to a continuum description of active particles with a recoil interaction in one dimension
• Dynamical crossovers and correlations in a harmonic chain of active particles
• Time-dependent properties of run-and-tumble particles: Density relaxation
• Fluctuations in the active Dyson Brownian motion and the overdamped Calogero-Moser model
• Inducing a bound state between active particles
• Counter-flow induced clustering: Exact results
• Emergent short-range repulsion for attractively coupled active particles
• Crossover dynamics and non-Gaussian fluctuations in inertial active chains
• Crystal to liquid cross-over for active particles with inverse-square power-law interaction
• Curvature-Driven Density and Fluctuations in Interacting AOUPs under Confinement
• Boundary layers, transport and universal distribution in boundary driven active systems
• From Attraction to Repulsion: Emergent Interactions in Harmonically Coupled Active Binary System