Derivation of Markovian master equations for spatially correlated decoherence

TL;DR

This paper develops a general formalism for deriving Markovian master equations that account for spatially correlated noise, enabling analysis without specific environmental models and including examples with non-trivial correlations.

Contribution

It introduces a universal approach to model spatially correlated Markovian noise and maps these equations to Lindblad form, broadening the understanding of decoherence processes.

Findings

Formalism describes spatial correlations without specific microscopic models

Method to map equations to Lindblad form for practical use

Examples of microscopic models with complex spatial-temporal correlations

Abstract

We introduce a general formalism to describe the effects of Markovian noise which is spatially correlated, typically decaying over some finite correlation length. For any system of interest, this formalism describes spatial correlations without the necessity to choose a particular microscopic model for the environment. We present a method of mapping the equations to Lindblad form and discuss functional forms for homogeneous spatial correlation functions. We also discuss two example microscopic models for the environment which exhibit non-trivial spatial-temporal correlation functions.