Classical Non-equilibrium Phases from a Quantum Perspective: Quasi-adiabatic evolution and Local Ansatz for Solving The Equilibrium State of Local Stochastic Dynamics

TL;DR

This paper explores the connection between non-equilibrium phases in stochastic dynamics and quantum phases using quasi-adiabatic evolution, matrix product operators, and an ansatz for local dynamics with detailed balance.

Contribution

It introduces a quantum perspective on non-equilibrium phases, deriving conditions for relating gapped quantum phases to stochastic dynamics and proposing a new ansatz for local stochastic processes.

Findings

Derived a condition linking quantum gapped phases with non-equilibrium dynamics

Developed an ansatz for local stochastic dynamics with a Matrix Product Representation

Established that the dynamics satisfy a generalized detailed balance

Abstract

Starting from a simple mapping of a generator of local stochastic dynamics to a quantum Hamiltonian, we derive a condition, which allows us to use the quasi-adiabatic evolution and so relate gapped quantum phases with non-equilibrium's. This leads us to a study of invertible matrix product operators. Finally, we present an ansatz for constructing local stochastic dynamics for which the Perron-Frobenius vector has a Matrix Product Representation. Additionally, we get for free that the dynamics satisfy a generalized form of detailed balance.