Diffusion with resetting in a logarithmic potential

Area of Science:

• Statistical Physics
• Non-equilibrium Systems
• Stochastic Processes

Background:

• Diffusion processes are fundamental in physics and biology.
• Resetting mechanisms introduce non-equilibrium dynamics to diffusion.
• Logarithmic potentials are relevant in various physical phenomena.

Purpose of the Study:

• To investigate the impact of resetting on diffusion in a logarithmic potential.
• To analyze the transitions and behaviors of the system as a function of potential strength and resetting rate.
• To generalize existing models of diffusion with resetting.

Main Methods:

• Analytical treatment of a particle diffusing in a logarithmic potential with a constant resetting rate.
• Characterization of non-equilibrium steady states for repulsive potentials.
• Derivation of closed-form expressions for first-passage time distributions for attractive/weakly repulsive potentials.

Main Results:

• A strongly repulsive logarithmic potential (βU₀ < -1) leads to a non-equilibrium steady state upon resetting.
• For weakly repulsive or attractive potentials (βU₀ > -1), resetting can expedite arrival at the origin.
• A resetting transition occurs at βU₀ = 5, where resetting is beneficial for -1 < βU₀ < 5 but detrimental for βU₀ > 5.

Conclusions:

• The study provides a comprehensive analysis of diffusion with resetting in a logarithmic potential.
• The findings reveal critical transitions and a resetting transition point, offering insights into optimizing search strategies.
• This work extends the applicability of resetting diffusion models to more complex potential landscapes.