Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability

Abstract

Quantum coherences characterise the ability of particles to quantum mechanically interfere within some given distances. In the context of noisy many-body quantum systems these coherences can fluctuate. A simple toy model to study such fluctuations in an out-of-equilibrium setting is the open quantum symmetric simple exclusion process (Q-SSEP) which describes spinless fermions in one dimension hopping to neighbouring sites with random amplitudes coupled between two reservoirs. Here we show that the dynamics of fluctuations of coherences in Q-SSEP have a natural interpretation as free cumulants, a concept from free probability theory. Based on this insight we provide heuristic arguments why we expect free probability theory to be an appropriate framework to describe coherent fluctuations in generic mesoscopic systems where the noise emerges from a coarse-grained description. In the case of Q-SSEP we show how the link to free probability theory can be used to derive the time evolution of connected fluctuations of coherences as well as a simple steady state solution.

17 pages main text, 13 pages appendices. This paper has been submitted simultaneously with "Eigenstate Thermalization Hypothesis and Free Probability" by S. Pappalardi, L. Foini and J. Kurchan where the relation between these two frameworks is discussed

References in corpus (5)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• Eigenstate Thermalization Hypothesis and Free Probability
• Can the Macroscopic Fluctuation Theory be Quantized?

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