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Anomalous current fluctuations from Euler hydrodynamics.

Takato Yoshimura1,2, Žiga Krajnik3

  • 1All Souls College, Oxford OX1 4AL, United Kingdom.

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Summary
This summary is machine-generated.

We investigated anomalous current fluctuations in charged cellular automata using hydrodynamic theory. Initial fluctuations explain most anomalies, but stochastic effects add unique contributions to typical fluctuations.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Complex Systems

Background:

  • Anomalous fluctuations in charge transport are crucial in non-equilibrium systems.
  • Stochastic cellular automata offer a tractable model for studying complex transport phenomena.

Purpose of the Study:

  • To explore the hydrodynamic origin of anomalous current fluctuations in stochastic charged cellular automata.
  • To analyze both large and typical fluctuations of charge current.
  • To compare results with the deterministic single-file limit.

Main Methods:

  • Ballistic macroscopic fluctuation theory (MFT).
  • Analysis of Euler equations for initial fluctuation propagation.
  • Comparison with microscopic results from the deterministic single-file limit.
  • Numerical simulations for stochastic models.

Main Results:

  • Initial fluctuations propagated by Euler equations generally characterize anomalous fluctuations at both large and typical scales.
  • A novel, additional contribution to typical fluctuations was identified in the stochastic case.
  • The conjectured functional form of the typical probability distribution aligns with numerical simulations.

Conclusions:

  • Hydrodynamic descriptions, particularly MFT, are powerful tools for understanding anomalous transport.
  • Stochasticity introduces unique features in fluctuation distributions beyond deterministic limits.
  • The study provides a theoretical framework and numerical validation for anomalous current fluctuations in these models.