Exact fluctuation and long-range correlations in a single-file model under resetting.

Area of Science:

• Statistical Physics
• Complex Systems
• Non-equilibrium Dynamics

Background:

• Stochastic resetting is a renewal mechanism involving intermittent process repetition, influencing system behavior and search processes.
• Understanding resetting's impact on complex systems, particularly particle dynamics, is crucial for non-equilibrium statistical mechanics.

Purpose of the Study:

• To investigate the effects of stochastic resetting on the dynamics of tracer particles in a one-dimensional random average process (RAP).
• To analytically compute key statistical properties like variance and correlations for both symmetric and asymmetric particle movement under resetting.

Main Methods:

• Analytical computation of variance, equal-time correlations, autocorrelation, and unequal-time correlations for tracer particles in a 1D RAP.
• Focus on comparing dynamics with and without stochastic resetting, and between symmetric and asymmetric particle movement.
• Validation of analytical findings through extensive numerical simulations.

Main Results:

• Stochastic resetting leads to distinct behaviors depending on particle movement symmetry (symmetric vs. asymmetric).
• Asymmetric movement under resetting induces long-range correlations absent in reset-free systems.
• Variance exhibits unique scaling behaviors: decay as ~e^{-rt}/sqrt[t] for symmetric and ~te^{-rt} for asymmetric cases (r = resetting rate).

Conclusions:

• Stochastic resetting significantly alters the statistical properties of 1D RAP, with outcomes strongly dependent on particle movement directionality.
• The study reveals novel correlation patterns and variance scalings induced by resetting, particularly in asymmetric scenarios.
• Analytical and numerical results provide a comprehensive understanding of resetting's influence on single-file systems.