Time-dependent density of diffusion with stochastic resetting is invariant to return speed

Area of Science:

• Physics
• Statistical Mechanics
• Physical Chemistry

Background:

• The standard Evans-Majumdar model assumes instantaneous resetting, neglecting real-world travel time.
• Diffusion with stochastic resetting models various physical processes.

Purpose of the Study:

• To investigate diffusion with resetting to the origin at a finite speed.
• To analyze the impact of finite return time on diffusion dynamics.

Main Methods:

• Mathematical modeling of diffusion with finite-speed resetting.
• Analysis of the time-dependent position distribution.

Main Results:

• A coupling arises between the resetting position and return time.
• The diffusive and return phases exhibit unique relaxation behaviors.
• The particle's position distribution is invariant to the return speed.

Conclusions:

• Finite return speed does not alter the steady-state results of diffusion with instantaneous resetting.
• The model provides a more realistic description of diffusion with resetting.