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.

46 pages, 3 figures

References in corpus (3)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• The entanglement membrane in chaotic many-body systems
• The Exclusion Process: A paradigm for non-equilibrium behaviour

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• $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
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