Fick-Jacobs description and first passage dynamics for diffusion in a channel under stochastic resetting

Area of Science:

• Physics
• Chemistry
• Surface Science
• Biophysics

Background:

• Particle transport through channels is crucial for various scientific fields and real-world applications.
• Understanding particle transition paths, lifetimes, and escape probabilities provides key insights.

Purpose of the Study:

• To investigate diffusive transport of Brownian particles in a conical channel with stochastic resetting.
• To extend Fick-Jacobs theory to account for resetting-induced transport dynamics.

Main Methods:

• Extension of Fick-Jacobs theory to incorporate stochastic resetting.
• Derivation of exact analytical expressions for transport statistics.
• Validation through three-dimensional Brownian dynamics simulations.

Main Results:

• Stochastic resetting can significantly expedite particle transport through channels.
• Exact expressions for conditional mean first passage times and escape probabilities were derived.
• A minimal average particle lifetime in the channel can be achieved by tuning the resetting rate, which exhibits transitions.

Conclusions:

• Stochastic resetting is a viable strategy to enhance particle transport efficiency in confined geometries.
• The findings have potential implications for facilitating particle transport across biological membranes.
• This study provides a theoretical framework for understanding resetting-enhanced transport phenomena.