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We analyzed tracer particle motion on a lattice with obstacles. Interactions introduce logarithmic terms and alter velocity decay, differing from impurity-free systems.

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Nonlinear dynamics

Background:

  • Understanding particle transport in disordered systems is crucial.
  • Linear response theory often fails to capture complex dynamics.

Purpose of the Study:

  • To determine the nonlinear time-dependent response of a tracer on a lattice with obstacles.
  • To investigate the effects of random obstacles on particle dynamics under an applied force.

Main Methods:

  • Exact calculation to first order in obstacle density.
  • Analysis of nonlinear drift velocity and steady-state behavior.
  • Comparison with stochastic simulations to validate results.

Main Results:

  • Interactions with obstacles introduce logarithmic contributions beyond the linear regime.
  • The long-time velocity decay is exponentially fast, unlike power-law relaxation in clean systems.
  • Deviations from linear response theory become significant due to impurity scattering.

Conclusions:

  • Random obstacles fundamentally alter tracer dynamics on lattices.
  • Nonlinear effects and impurity interactions lead to distinct transport properties.
  • The study provides an exact analytical framework for disordered systems.