Stochastic jump processes for non-Markovian quantum dynamics

TL;DR

This paper introduces a stochastic jump process framework for non-Markovian quantum dynamics, revealing how memory effects influence quantum state evolution and linking positivity violations to singularities in the stochastic equations.

Contribution

It develops a stochastic Schrödinger equation for non-Markovian systems, providing new insights into their dynamics and the structural conditions for positivity.

Findings

Non-Markovian effects manifest in statistical correlations.

Violations of positivity relate to singularities in the stochastic equations.

The approach offers a new perspective on non-Markovian quantum master equations.

Abstract

It is shown that non-Markovian master equations for an open system which are local in time can be unravelled through a piecewise deterministic quantum jump process in its Hilbert space. We derive a stochastic Schr\"odinger equation that reveals how non-Markovian effects are manifested in statistical correlations between different realizations of the process. Moreover, we demonstrate that possible violations of the positivity of approximate master equations are closely connected to singularities of the stochastic Schr\"odinger equation, which could lead to important insights into the structural characterization of positive non-Markovian equations of motion.