Random Walks on Comb-like Structures under Stochastic Resetting

Area of Science:

• Statistical Physics
• Complex Systems

Background:

• Random walks are fundamental models in statistical physics.
• Comb structures present unique challenges due to their branching nature.
• Stochastic resetting introduces non-equilibrium dynamics to random processes.

Purpose of the Study:

• To investigate the long-time dynamics of mean squared displacement (MSD) for a random walker on a comb structure.
• To analyze the impact of different stochastic resetting strategies (global and local) on walker dynamics.
• To understand the interplay between diffusion, waiting times, and resetting processes.

Main Methods:

• Theoretical analysis of mean squared displacement (MSD).
• Modeling random walker motion on a comb lattice with diffusive backbone and finger jumps.
• Considering both Markovian and non-Markovian resetting mechanisms.
• Analyzing global resetting (any point to origin) and local resetting (finger to backbone).

Main Results:

• Markovian local resetting induces normal diffusion, mitigating finger trapping.
• Non-Markovian local resetting shows a crossover with three regimes: two subdiffusive and one diffusive.
• Global resetting prevents normal diffusion, leading to constant MSD (Markovian) or subdiffusion (non-Markovian).

Conclusions:

• Stochastic resetting significantly alters random walk behavior on comb structures.
• The type of resetting (local/global) and its temporal nature (Markovian/non-Markovian) dictate the diffusion regime.
• This study reveals complex dynamics arising from the interplay of diffusion, trapping, and resetting in heterogeneous environments.