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arXiv · 1505.00982

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

Benoît Descamps·Frank Verstraete
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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.

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Benoît Descamps, Frank Verstraete. 2015-05-05. Classical Non-equilibrium Phases from a Quantum Perspective: Quasi-adiabatic evolution and Local Ansatz for Solving The Equilibrium State of Local Stochastic Dynamics. https://arxiv.org/abs/1505.00982

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