Hard core run and tumble particles on a one dimensional lattice

Abstract

We study the large scale behavior of a collection of hard core run and tumble particles on a one dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin variable until the direction of spin is reversed. We map the run and tumble model to a mass transfer model with fluctuating directed bonds. We calculate the steady state single site mass distribution in the mass model within a mean field approximation for larger spin-flip rates and by analyzing an appropriate coalescence fragmentation model for small spin-flip rates. We also calculate the hydrodynamic coefficients of diffusivity and conductivity for both large and small spin-flip rates and show that the Einstein relation is violated in both regimes. We also show how the non-gradient nature of the process can be taken into account in a systematic manner to calculate the hydrodynamic coefficients.

arXiv comment23 pages, 18 figures

References in corpus (45)

• Novel type of phase transition in a system of self-driven particles
• Flocks, herds, and schools: A quantitative theory of flocking
• Athermal Phase Separation of Self-Propelled Particles with no Alignment
• Onset of collective and cohesive motion
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Long-lived Giant Number Fluctuations in a Swarming Granular Nematic
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Pressure is not a state function for generic active fluids
• Diffusive transport without detailed balance in motile bacteria: Does microbiology need statistical physics?
• A continuum theory of phase separation kinetics for active Brownian particles
• Active matter
• Collective motion and nonequilibrium cluster formation in colonies of gliding bacteria
• Fluctuations in Stationary non Equilibrium States
• 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
• The Physics of the Vicsek Model
• Revisiting the flocking transition using active spins
• Active Brownian Motion in Two Dimensions
• Run-and-tumble in a crowded environment: persistent exclusion process for swimmers
• Jamming and Attraction of Interacting Run-and-Tumble Random Walkers
• Run-and-Tumble Dynamics of Self-Propelled Particles in Confinement
• Exact Hydrodynamic Description of Active Lattice Gases
• Microscopic versus macroscopic approaches to non-equilibrium systems
• 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
• From single-particle to collective effective temperatures in an active fluid of self-propelled particles
• Phase separation and large deviations of lattice active matter
• Non-crossing run-and-tumble particles on a line
• Exact Calculation of the Spatio-temporal Correlations in the Takayasu model and in the q-model of Force Fluctuations in Bead Packs
• 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
• Universal scaling in active single-file dynamics
• Exact Tagged Particle Correlations in the Random Average Process
• Flocking Regimes in a Simple Lattice Model
• Coarsening and clustering in run-and-tumble dynamics with short-range exclusion
• Toward the full short-time statistics of an active Brownian particle on the plane
• Gap statistics of two interacting run and tumble particles in one dimension
• Kang-Redner Anomaly in Cluster-Cluster Aggregation
• Additivity, density fluctuations, and nonequilibrium thermodynamics for active Brownian particles
• Center of mass perturbation as a normalizable estimate of dynamic balance in gait: an application comparing typically developing children with spastic cerebral palsy
• Einstein relation and hydrodynamics of nonequilibrium mass transport processes
• Hydrodynamics, superfluidity and giant number fluctuations in a model of self-propelled particles
• Additivity property and emergence of power laws in nonequilibrium steady states
• Conserved Mass Models and Particle Systems in One Dimension
• Additivity and density fluctuations in Vicsek-like models of self-propelled particles

Cited by in corpus (20)

• Attractor-driven matter
• Nonexistence of motility induced phase separation transition in one dimension
• Current fluctuations in an interacting active lattice gas
• Interacting, running and tumbling: the active Dyson Brownian motion
• A Monte Carlo algorithm to measure probabilities of rare events in cluster-cluster aggregation
• Pushing run-and-tumble particles through a rugged channel
• How motility affects Ising transitions
• Time-dependent properties of run-and-tumble particles: Density relaxation
• Fluctuations in the active Dyson Brownian motion and the overdamped Calogero-Moser model
• Transport and fluctuations in mass aggregation processes: mobility driven clustering
• Geometric and Nonequilibrium Criticality in Run-and-Tumble Particles with Competing Motility and Attraction
• Site-percolation transition of run-and-tumble particles
• Non-equilibrium phase transitions in active rank diffusions
• Counter-flow induced clustering: Exact results
• Tracer dynamics in the active random average process
• Fluctuating Hydrodynamics Describes Transport in Cellular Aggregates
• Persistent exclusion process with time-periodic drive
• Crystal to liquid cross-over for active particles with inverse-square power-law interaction
• Insertion space in repulsive active matter
• Density-dependent transport coefficients in two-dimensional cellular aggregates