Stochastic Schr\"odinger equations and memory

TL;DR

This paper extends stochastic Schr"odinger equations to include memory effects using colored noise, providing a framework for non-Markovian quantum dynamics and connecting to master equations with memory kernels.

Contribution

It introduces a non-Markovian extension of stochastic Schr"odinger equations using colored noise and demonstrates their relation to master equations with memory effects.

Findings

Non-Markovian stochastic Schr"odinger equations can be derived with colored noise.

Under certain conditions, the evolution reduces to a random Hamiltonian.

The equations unravel master equations with memory kernels.

Abstract

By starting from the stochastic Schr\"odinger equation and quantum trajectory theory, we introduce memory effects by considering stochastic adapted coefficients. As an example of a natural non-Markovian extension of the theory of white noise quantum trajectories we use an Ornstein-Uhlenbeck coloured noise as the output driving process. Under certain conditions a random Hamiltonian evolution is recovered. Moreover, we show that our non-Markovian stochastic Schr\"odinger equations unravel some master equations with memory kernels.