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We studied active lattice walks, a type of biased random walk. Our findings reveal distinct diffusive behaviors and persistent cross-correlations in two dimensions, confirmed by simulations.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Stochastic Processes

Background:

  • Continuous time random walks (CTRWs) are fundamental models for particle transport.
  • Active particles exhibit self-propulsion, leading to non-equilibrium dynamics.
  • Understanding diffusion in lattice systems is crucial for various physical phenomena.

Purpose of the Study:

  • To investigate the behavior of active lattice walks in one and two dimensions.
  • To derive exact results for occupation probabilities and large deviation functions.
  • To analyze the influence of orientational diffusion on particle dynamics.

Main Methods:

  • Analytical derivation of occupation probabilities in the continuum limit.
  • Computation of the large deviation free-energy function.
  • Kinetic Monte Carlo simulations for verification.

Main Results:

  • Exact results for occupation probabilities and late-time cumulants of displacements.
  • Demonstration of persistent cross-correlations in 2D active lattice walks.
  • Identification of two distinct diffusive regimes in the large deviation function.

Conclusions:

  • Active lattice walks exhibit complex dynamics beyond simple diffusion.
  • Orientational diffusion significantly impacts particle displacement statistics.
  • Analytical and simulation results confirm the theoretical predictions.