Space-dependent diffusion with stochastic resetting: A first-passage study

Area of Science:

• Statistical Physics
• Non-equilibrium Systems
• Complex Systems

Background:

• Diffusion processes are fundamental in physics and biology.
• Spatially dependent diffusion and external potentials significantly alter particle dynamics.
• Stochastic resetting introduces non-Markovian behavior, impacting first-passage times.

Purpose of the Study:

• To investigate the influence of stochastic resetting on first-passage properties of biased diffusion with space-dependent diffusion coefficients.
• To analytically derive survival probabilities and first-passage time distributions.
• To characterize dynamical transitions and phase diagrams influenced by resetting.

Main Methods:

• Analytical derivation of survival probability in Laplace space.
• Analysis of first-passage time distribution in a limiting case.
• Construction of a phase diagram based on the parameter ν = (1 + μD₀^-1).

Main Results:

• An exact expression for survival probability and first-passage time distribution was derived.
• The system exhibits dynamical transitions governed by the parameter ν.
• A resetting transition occurs at ν = 3, altering the efficiency of first-passage.
• For repulsive potentials (ν < 0), the origin is unreachable; for attractive potentials (ν > 0), it is eventually reached.

Conclusions:

• Stochastic resetting introduces a tunable transition point (ν = 3) that can either accelerate or hinder first-passage.
• The interplay between drift, diffusion, and resetting dictates the system's long-term behavior.
• This work provides a foundation for studying resetting phenomena in more complex, inhomogeneous diffusion systems.