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Multidimensional stationary probability distribution for interacting active particles.

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This study introduces a new theory for non-equilibrium systems with colored noise, accurately predicting active particle behavior around obstacles and deriving an equation of state.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Active Matter

Background:

  • Understanding the dynamics of systems with colored noise is crucial.
  • Active particles exhibit complex behaviors, especially around obstacles.

Purpose of the Study:

  • To derive the stationary probability distribution for non-equilibrium systems with Gaussian colored noise.
  • To quantitatively describe active particle accumulation around repulsive obstacles.

Main Methods:

  • Multidimensional Unified Colored Noise Approximation.
  • Comparison of theoretical predictions with numerical simulations.

Main Results:

  • The derived probability density accurately models active particle accumulation.
  • The probability of close contact between repulsive particles decreases when one is pinned.
  • Radial density profiles show non-trivial scaling for isotropic potentials.

Conclusions:

  • The theory provides a quantitative description of active particle systems.
  • The derived framework allows for the formulation of an equation of state for these systems.