Quantum Scaling Approach to Nonequilibrium Models

TL;DR

This paper introduces a quantum scaling method for analyzing nonequilibrium exclusion models, leveraging quantum-classical mappings and symmetries to find exact fixed points and reformulate models in classical Hamiltonian terms.

Contribution

It develops a real space scaling approach for nonequilibrium models that incorporates conservation laws and duality, providing exact solutions and novel reformulations.

Findings

Exact fixed points for various exclusion models

Quantum-classical mapping of nonequilibrium systems

Reformulation of asymmetric exclusion process as classical Hamiltonian

Abstract

Stochastic nonequilibrium exclusion models are treated using a real space scaling approach. The method exploits the mapping between nonequilibrium and quantum systems, and it is developed to accommodate conservation laws and duality symmetries, yielding exact fixed points for a variety of exclusion models. In addition, it is shown how the asymmetric simple exclusion process in one dimension can be written in terms of a classical Hamiltonian in two dimensions using a Suzuki-Trotter decomposition.