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Diffusion with stochastic resetting on a lattice.

Alexander K Hartmann1, Satya N Majumdar2

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Summary
This summary is machine-generated.

We derived an exact formula for particle diffusion on lattices with resetting. The mean first-passage time shows unique behavior on lattices, differing from continuous models, especially near the target.

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Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Mathematical Physics

Background:

  • Particle diffusion is fundamental in various scientific fields.
  • Continuous models often simplify lattice-based diffusion phenomena.
  • Understanding diffusion with resetting is crucial for optimizing search strategies.

Purpose of the Study:

  • To derive an exact formula for the mean first-passage time (MFPT) of a diffusing particle on a d-dimensional hypercubic lattice with resetting.
  • To explore lattice-specific effects on diffusion and resetting dynamics.
  • To compare lattice results with existing continuum theories.

Main Methods:

  • Exact analytical formula derivation for MFPT.
  • Analysis of scaling limits to recover continuous space results.
  • Investigation of parameter space including lattice dimensions and resetting rates.
  • Numerical simulations for verification.

Main Results:

  • An exact formula for MFPT on lattices with resetting was obtained, valid for all parameters.
  • Lattice-specific MFPT behavior was observed, diverging at low and high resetting rates with a minimum in between.
  • A unique power-law divergence of MFPT with an exponent dependent on the starting position was found.
  • For nearest neighbors of the target, MFPT monotonically decreases with resetting rate, approaching a universal limit.

Conclusions:

  • Lattice diffusion with resetting exhibits unique phenomena not captured by continuum theories.
  • The starting position significantly influences MFPT, especially its divergence exponent.
  • Resetting strategies can be optimized based on lattice geometry and target proximity.