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Stochastic resetting profoundly impacts systems, influencing particle dynamics in a one-dimensional random average process. Resetting creates distinct behaviors for symmetric vs. asymmetric particle movement, altering correlations and variance.

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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.