Condensed Matter > Statistical Mechanics
[Submitted on 25 Apr 2022 (v1), last revised 31 Mar 2023 (this version, v4)]
Title:Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
View PDFAbstract: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.
Submission history
From: Ludwig Hruza [view email][v1] Mon, 25 Apr 2022 14:19:01 UTC (308 KB)
[v2] Wed, 4 May 2022 16:54:51 UTC (308 KB)
[v3] Mon, 5 Dec 2022 21:19:53 UTC (1,376 KB)
[v4] Fri, 31 Mar 2023 13:01:26 UTC (876 KB)
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