Non-Markovian quantum trajectories: an exact result

TL;DR

This paper provides an exact solution to the non-Markovian stochastic Schrödinger equation for a free particle, revealing how noise correlation affects quantum dynamics in collapse models and continuous measurement scenarios.

Contribution

It presents the first explicit general solution for the non-Markovian stochastic Schrödinger equation in the free particle case, including analysis of exponential noise correlations.

Findings

Explicit general solution for free particle case

Quantitative description of dynamics with exponential noise correlation

Analysis of dependence on noise correlation time

Abstract

We analyze the non-Markovian stochastic Schroedinger equation describing a particle subject to spontaneous collapses in space (in the language of collapse models), or subject to a continuous measurement of its position (in the language of continuous quantum measurement). For the first time, we give the explicit general solution for the free particle case (H = p^2/2m), and discuss the main properties. We analyze the case of an exponential correlation function for the noise, giving a quantitative description of the dynamics and of its dependence on the correlation time.