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

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.

Automated summary

The research presents a solution for the invariant probability measure of the one-dimensional Q-SSEP model by constructing steady correlation functions of the system density matrix and quantum expectation values. These correlation functions contain rich structures of fluctuating quantum correlations and coherences, based on an interplay between permutation groups and polynomials rather than standard techniques from the theory of integrable systems. Additionally, a possible combinatorial interpretation of the Q-SSEP correlation functions is pointed out through a surprising connection with geometric combinatorics and associahedron polytopes.