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

• URL: http://arxiv.org/abs/2006.12222v2
• Date: Wed, 7 Apr 2021 10:50:08 GMT
• Title: Solution to the Quantum Symmetric Simple Exclusion Process : the Continuous Case
• Authors: Denis Bernard and Tony Jin
• Abstract summary: We present a solution for the invariant probability measure of the one dimensional Q-SSEP in the infinite size limit. We incidentally point out a possible interpretation of the Q-SSEP correlation functions via a surprising conneatorics and the associahedron polytopes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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