Drift-diffusive resetting search process with stochastic returns: Speedup beyond optimal instantaneous return.

Area of Science:

• Physics
• Statistical Mechanics
• Nonlinear Dynamics

Background:

• Stochastic resetting is a strategy to reduce completion times in first-passage processes.
• Instantaneous resetting is practically infeasible; finite-time return is a more realistic generalization.
• Previous studies showed finite-time stochastic returns speed up diffusive processes with diverging mean completion times.

Purpose of the Study:

• Investigate if finite-time stochastic returns can speed up first-passage processes with finite mean completion times.
• Analyze a 1D drift-diffusion search process with stochastic resetting and a potential U(x)=λ|x|.
• Compare the performance of stochastic return against instantaneous resetting and the underlying process.

Main Methods:

• Exact computation of the mean first-passage time for the drift-diffusion process with stochastic resetting.
• Analysis of system characteristics concerning resetting rate and potential strength.
• Identification of parameter regions where stochastic return offers advantages.

Main Results:

• A unified phase space was identified, revealing parameter regions where stochastic return outperforms both the underlying process and instantaneous resetting.
• For certain parameters, stochastic return achieved lower mean completion times than optimally restarted instantaneous processes.
• The study demonstrates the effectiveness of stochastic return protocols in optimizing first-passage times.

Conclusions:

• Stochastic resetting with finite-time returns is a potent optimization strategy for first-passage processes.
• This method offers significant advantages over instantaneous resetting, particularly for processes with finite mean completion times.
• The findings suggest stochastic return protocols can serve as a superior alternative to classical first-passage under resetting.