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

TL;DR

This paper provides an exact solution for the invariant measure of the one-dimensional Quantum Symmetric Simple Exclusion Process, revealing complex quantum correlations and a novel combinatorial interpretation.

Contribution

It introduces a new method to solve for the steady state of Q-SSEP using permutation groups and polynomials, without relying on integrable systems techniques.

Findings

Explicit steady correlation functions for Q-SSEP

Discovery of quantum correlations and coherences in the invariant measure

Connection between Q-SSEP correlations and geometric combinatorics

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.