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Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
1Max-Planck Institute for the Physics of Complex Systems, cfAED and GISC, Nöthnitzer Straße 38, 01187 Dresden, Germany.
Physical Review. E
|September 28, 2017
Summary
Stochastic resetting enhances Brownian particle confinement. Energy-dependent resetting in a harmonic potential is more effective than parameter quenches for faster spatial confinement.
Area of Science:
- Statistical mechanics
- Non-equilibrium physics
- Complex systems
Background:
- Brownian motion describes particle diffusion influenced by random forces.
- Stochastic resetting introduces a mechanism to return particles to a specific location.
- Understanding resetting dynamics is crucial for controlling diffusion processes.
Purpose of the Study:
- To develop a systematic approach for analyzing Brownian particle dynamics with space-dependent stochastic resetting.
- To derive analytical expressions for key statistical properties of resetting processes.
- To explore novel resetting dynamics, including energy-dependent rates.
Main Methods:
- Path integral formulation to describe particle trajectories.
- Renewal theory to analyze the impact of resetting events.
- Derivation of analytical expressions for propagators, first-reset time distributions, and long-time spatial distributions.
Main Results:
- Analytical expressions for various statistics of resetting dynamics were derived.
- A novel resetting process for a Brownian particle in a harmonic potential with energy-dependent rates was analyzed.
- Energy-dependent resetting proved more efficient for spatial confinement than parameter quenches.
Conclusions:
- The developed framework provides a powerful tool for studying complex resetting phenomena.
- Energy-dependent stochastic resetting offers a superior strategy for rapid spatial confinement of diffusing particles.
- This work opens new avenues for controlling and optimizing diffusion processes in various physical and biological systems.
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