Derivation of Markovian master equations for spatially correlated decoherence

Understand

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.