Resetting by rescaling: Exact results for a diffusing particle in one dimension.

Area of Science:

• Statistical Physics
• Nonlinear Dynamics

Background:

• Diffusive particle transport is fundamental in physics and biology.
• Stochastic resetting introduces non-equilibrium dynamics, altering search strategies.
• Rescaling particle positions offers a novel approach to control diffusion.

Purpose of the Study:

• To investigate a diffusive particle model with stochastic resetting via position rescaling.
• To analyze the long-time position distribution and mean first-passage time (MFPT).
• To compare the efficiency of positive and negative rescaling strategies for target search.

Main Methods:

• Exact computation of the stationary position distribution for |a|<1.
• Solving a nonlocal second-order differential equation for the MFPT.
• Analytical solutions for 0≤a<1 and -1
• Analysis of MFPT as a function of resetting rate r and rescaling factor a.

Main Results:

• The position distribution is Gaussian near the origin and decays exponentially for large distances.
• MFPT exhibits a minimum at a specific resetting rate r*(a) for all -1
• Optimized MFPT increases monotonically with a for -1
• Negative rescaling (a<0) significantly expedites target search compared to standard resetting (a=0).

Conclusions:

• Stochastic resetting with position rescaling provides a tunable mechanism to control particle diffusion.
• Negative rescaling, incorporating a reflection, is a beneficial strategy for accelerating target detection in one dimension.
• This method offers advantages over standard resetting to the origin for search optimization.