Local Master Equation for Small Temperatures

TL;DR

This paper introduces a local Master equation framework for open quantum systems at low temperatures, applicable in both Markovian and non-Markovian regimes, with improved validity over Lindblad equations and efficient simulation for low bond dimension states.

Contribution

It presents a novel local Master equation applicable at low temperatures that extends the validity beyond traditional Lindblad equations and enables efficient simulation of certain quantum states.

Findings

The local Master equation is valid at low temperatures without requiring exponentially weak coupling.

Both Markovian and non-Markovian forms are developed.

Simulation complexity is polynomial in system size for low bond dimension states.

Abstract

We present a local Master equation for open system dynamics in two forms: Markovian and non-Markovian. Both have a wider range of validity than the Lindblad equation investigated by Davies. For low temperatures, they do not require coupling to be exponentially weak in the system size. If the state remains a low bond dimension Matrix Product State throughout the evolution, the local equation can be simulated in time polynomial in system size.