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Ratcheting by Stochastic Resetting With Fat-Tailed Time Distributions
Jianli Liu1, Yunyun Li1, Pulak K Ghosh2
1IMOE Key Laboratory of Advanced Mico-Structured Materials and Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Science and Engineering, Tongji University, Shanghai, 200092, China.
Summary
Stochastic resetting with fat-tailed distributions can enable Brownian particle rectification in ratchet potentials. Optimal drift occurs with finite, large mean resetting times, leading to superdiffusive motion.
Area of Science:
- Statistical physics
- Non-equilibrium systems
- Complex systems
Background:
- Brownian motion describes random particle movement.
- Ratchet potentials create directed motion from random fluctuations.
- Stochastic resetting introduces periodic resets to particle trajectories.
Purpose of the Study:
- Investigate Brownian particle drift in a ratchet potential.
- Analyze the effect of stochastic resetting with fat-tailed distributions.
- Determine conditions for rectification and anomalous diffusion.
Main Methods:
- Numerical simulations of particle dynamics.
- Analytical treatment of stochastic processes.
- Analysis of Pareto-distributed resetting times with varying tail index β.
Main Results:
- Rectification observed for β > 2, even with infinite mean resetting time.
- Rectification suppressed for β < 2.
- Drift speed maximized for β slightly above 1 (finite, large mean resetting times).
- Transition from normal to superdiffusive diffusion observed.
Conclusions:
- Fat-tailed resetting distributions significantly alter Brownian particle behavior in ratchet potentials.
- Optimal drift and superdiffusion are linked to the tail properties of the resetting time distribution.
- The study highlights the importance of resetting time statistics in non-equilibrium systems.
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