Solution to the Quantum Symmetric Simple Exclusion Process : the Continuous Case

Abstract

The Quantum Symmetric Simple Exclusion Process (Q-SSEP) is a model for quantum stochastic dynamics of fermions hopping along the edges of a graph with Brownian noisy amplitudes and driven out-of-equilibrium by injection-extraction processes at a few vertices. We present a solution for the invariant probability measure of the one dimensional Q-SSEP in the infinite size limit by constructing the steady correlation functions of the system density matrix and quantum expectation values. These correlation functions code for a rich structure of fluctuating quantum correlations and coherences. Although our construction does not rely on the standard techniques from the theory of integrable systems, it is based on a remarkable interplay between the permutation groups and polynomials. We incidentally point out a possible combinatorial interpretation of the Q-SSEP correlation functions via a surprising connexion with geometric combinatorics and the associahedron polytopes.

arXiv comment46 pages, 3 figures

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• Dynamics of Fluctuations in Quantum Simple Exclusion Processes
• Impact of Dissipation on Universal Fluctuation Dynamics in Open Quantum Systems
• Can the Macroscopic Fluctuation Theory be Quantized?
• Designs via Free Probability
• Entanglement asymmetry dynamics in random quantum circuits
• Bernoulli variables, classical exclusion processes and free probability
• Universal out-of-equilibrium dynamics of 1D critical quantum systems perturbed by noise coupled to energy
• Spacetime picture for entanglement generation in noisy fermion chains
• Large deviations of density fluctuations in the boundary driven Quantum Symmetric Simple Inclusion Process
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• Structured random matrices and cyclic cumulants: A free probability approach
• $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
• Domain-wall melting in all-to-all QSSEP from random-matrix theory