Jump-diffusion unravelling of a non Markovian generalized Lindblad master equation

TL;DR

This paper develops jump-diffusion stochastic unravellings for non-Markovian generalized Lindblad equations, linking them to continuous measurement interpretations and exploring effects on a two-level system's heterodyne spectrum.

Contribution

It introduces a novel jump-diffusion unravelling framework for non-Markovian Lindblad equations, extending measurement interpretation and analyzing spectral effects.

Findings

Unravelling formulated as jump-diffusion SDEs for wave functions.

Measurement interpretation constrained by superselection rules.

Application to heterodyne spectrum of a two-level system with structured bath.

Abstract

The "correlated-projection technique" has been successfully applied to derive a large class of highly non Markovian dynamics, the so called non Markovian generalized Lindblad type equations or Lindblad rate equations. In this article, general unravellings are presented for these equations, described in terms of jump-diffusion stochastic differential equations for wave functions. We show also that the proposed unravelling can be interpreted in terms of measurements continuous in time, but with some conceptual restrictions. The main point in the measurement interpretation is that the structure itself of the underlying mathematical theory poses restrictions on what can be considered as observable and what is not; such restrictions can be seen as the effect of some kind of superselection rule. Finally, we develop a concrete example and we discuss possible effects on the heterodyne spectrum of a two-level system due to a structured thermal-like bath with memory.