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Exact Anomalous Current Fluctuations in a Deterministic Interacting Model
Žiga Krajnik1, Johannes Schmidt2,3, Vincent Pasquier4
1Faculty for Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, 1000 Ljubljana, Slovenia.
Physical Review Letters
|May 6, 2022
Summary
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.
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.
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