Work

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

Year: 2021

Type: article

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.

Source: Communications in Mathematical Physics

DOI: 10.1007/s00220-021-04087-x

Authors: Denis Bernard, Tony Jin

Institutions: Centre National de la Recherche Scientifique, École Normale Supérieure - PSL, Sorbonne Université, Laboratoire de Physique de l'Ecole Normale Supérieure, University of Geneva

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,690

Funders: Agence Nationale de la Recherche, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Université de Genève