Active particle in one dimension subjected to resetting with memory.

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• Diffusion processes with memory effects, particularly preferential return mechanisms, are increasingly studied.
• Standard diffusive particles intermittently reset to previously visited positions, with revisit probability proportional to time spent.

Purpose of the Study:

• To investigate an active version of the preferential return diffusion model with self-propulsion and telegraphic noise.
• To analyze the interplay between activity-driven ballistic motion and memory-induced anomalous diffusion.

Main Methods:

• Exact derivation of the position distribution in Fourier space.
• Analytical calculation of the position's variance over time.
• Investigation of the crossover dynamics between different regimes.
• Derivation of a large deviation principle for particle position.

Main Results:

• The active model exhibits a crossover from short-time ballistic behavior to long-time logarithmic diffusion.
• The position distribution and variance are derived exactly.
• A large deviation principle with logarithmic time scaling is established, differing from standard algebraic forms.
• At large distances, large deviations become time-independent, matching a specific nonequilibrium steady state.

Conclusions:

• The active preferential return model introduces complex non-Markovian dynamics due to both self-propulsion and memory.
• The study provides exact analytical results for position distribution and large deviations.
• The findings highlight unique scaling behaviors and steady-state properties in active matter systems with memory.