Anomalous current fluctuations from Euler hydrodynamics

Abstract

We consider the hydrodynamic origin of anomalous current fluctuations in a family of stochastic charged cellular automata. Using ballistic macroscopic fluctuation theory, we study both typical and large fluctuations of the charge current and reproduce microscopic results which are available for the deterministic single-file limit of the models. Our results indicate that in general initial fluctuations propagated by Euler equations fully characterize both scales of anomalous fluctuations. For stochastic dynamics, we find an additional contribution to typical fluctuations and conjecture the functional form of the typical probability distribution, which we confirm by numerical simulations.

v1:6 + 17 pages, 2 + 2 figures, v2:minor changes, additional references, v3: final version, results on the diffusion constant, which will be reported elsewhere, dropped from supplemental materials (now incorporated in the main text as Appendices), the typos on the location of the absolute value in Eqs. (C4, C5) fixed (these typos were unnoticed in the published version)

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• Diffusive hydrodynamics from long-range correlations
• Simulating generalised fluids via interacting wave packets evolution
• Fluctuations of stochastic charged cellular automata
• Hydrodynamic fluctuations of stochastic charged cellular automata
• Macroscopic Quantum States and Universal Correlations in a Disorder-Order Interface Propagating over a 1D Ground State