English

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