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Area of Science:

  • Physics
  • Statistical Mechanics
  • Non-equilibrium systems

Background:

  • Stochastic processes like diffusion and subdiffusion are fundamental in nature.
  • Understanding the impact of external interventions, such as resetting, is crucial.
  • Stochastic resetting introduces a mechanism to interrupt and restart a process.

Purpose of the Study:

  • To investigate the influence of stochastic resetting on diffusion and subdiffusion.
  • To determine the conditions under which these processes reach a steady state.
  • To characterize the probability density function (PDF) and relaxation behavior.

Main Methods:

  • Analysis of mean squared displacement under resetting.
  • Derivation of the PDF in Laplace space for subdiffusion.
  • Investigation of steady-state properties and relaxation rates.

Main Results:

  • Diffusion reaches a constant mean squared displacement only with finite mean and variance of reset times.
  • A cusp is observed in the Gaussian propagator's PDF for diffusion under resetting.
  • For subdiffusion, the PDF is derived in Laplace space, and a steady state is possible even with finite mean reset times.

Conclusions:

  • Stochastic resetting significantly alters diffusion and subdiffusion dynamics.
  • Finite mean and variance of reset times are key for stabilizing diffusion.
  • Subdiffusion can exhibit steady states under resetting protocols with finite mean reset times.