Current fluctuations in noninteracting run-and-tumble particles in one dimension

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Non-equilibrium Systems

Background:

• Understanding particle transport is crucial in diverse fields, from biophysics to materials science.
• Non-interacting particle systems provide fundamental models for complex phenomena.
• Investigating flux distributions reveals insights into system dynamics and emergent behaviors.

Purpose of the Study:

• To develop a general framework for studying the flux distribution through the origin in 1D systems.
• To analyze both diffusive (passive) and run-and-tumble (active) particle dynamics.
• To examine annealed and quenched initial conditions and their impact on flux distributions.

Main Methods:

• Development of a general theoretical framework for flux distribution analysis.
• Exact computation of the mean flux in annealed cases using Green's functions.
• Derivation of anomalous large-deviation forms for quenched run-and-tumble dynamics.
• Calculation of the rate function for large deviations and probabilities of rare events.
• Verification using importance sampling Monte Carlo simulations.

Main Results:

• Flux distribution is Poissonian in the annealed case for arbitrary dynamics.
• Quenched run-and-tumble dynamics exhibit anomalous large-deviation behavior at large times.
• The probability of no particles to the right of the origin decays as a stretched exponential for both dynamics.
• A nontrivial rate function for large deviations in the quenched case was computed.

Conclusions:

• The proposed framework provides a unified approach to studying flux distributions in 1D systems.
• Active particle dynamics (run-and-tumble) introduce significant deviations from passive (diffusive) behavior, especially in quenched scenarios.
• The study elucidates the statistical properties of particle flux and rare events in non-equilibrium systems.