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

Published inCommunications in Mathematical Physics, vol. 384, no. 2, p. 1141-1185
Publication date2021-04-21
First online date2021-04-21
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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BERNARD, Denis, JIN, Zizhuo Tony. Solution to the Quantum Symmetric Simple Exclusion Process: The Continuous Case. In: Communications in Mathematical Physics, 2021, vol. 384, n° 2, p. 1141–1185. doi: 10.1007/s00220-021-04087-x
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ISSN of the journal0010-3616
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