Classical Non-equilibrium Phases from a Quantum Perspective: Quasi-adiabatic evolution and Local Ansatz for Solving The Equilibrium State of Local Stochastic Dynamics
Quantum Physics
2015-12-10 v3
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.
Keywords
Cite
@article{arxiv.1505.00982,
title = {Classical Non-equilibrium Phases from a Quantum Perspective: Quasi-adiabatic evolution and Local Ansatz for Solving The Equilibrium State of Local Stochastic Dynamics},
author = {Benoît Descamps and Frank Verstraete},
journal= {arXiv preprint arXiv:1505.00982},
year = {2015}
}
Comments
Paper incomplete, will be updated in the future