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Exact Anomalous Current Fluctuations in a Deterministic Interacting Model.

Žiga Krajnik1, Johannes Schmidt2,3, Vincent Pasquier4

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We analyzed charge transfer fluctuations in interacting particles. Non-Gaussian distributions and singular scaled cumulants were observed, suggesting new dynamical universality classes in deterministic systems.

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Area of Science:

  • Statistical physics
  • Many-body systems
  • Complex systems

Background:

  • Understanding charge transfer dynamics is crucial in condensed matter and statistical physics.
  • Classical automata provide simplified models for complex interacting particle systems.
  • Full counting statistics offer insights into charge transport fluctuations.

Purpose of the Study:

  • To analytically compute the full counting statistics of charge transfer in a classical automaton.
  • To investigate charge current fluctuations across various timescales.
  • To identify novel dynamical universality classes in deterministic many-body systems.

Main Methods:

  • Analytical computation of the moment generating function for a stationary equilibrium state.
  • Asymptotic analysis to determine the structure of charge current fluctuations.
  • Investigation of cumulant behavior and properties of scaled cumulant generating functions.

Main Results:

  • A closed-form expression for the moment generating function was derived.
  • Non-Gaussian probability distributions for integrated charge current were found, even with diffusive susceptibility.
  • Higher-order cumulants exhibit indefinite growth, indicating singular scaled cumulants and a dynamical critical point.

Conclusions:

  • The study reveals unorthodox features in charge transfer fluctuations, including non-Gaussianity and singular scaled cumulants.
  • The findings suggest the existence of novel dynamical universality classes in deterministic many-body systems.
  • The research highlights the complex behavior of charge transport in classical automata.