Exact solution for a non-Markovian dissipative quantum dynamics

TL;DR

This paper presents an exact analytic solution for the stochastic Schrödinger equation of a harmonic oscillator in a non-Markovian, dissipative environment, advancing the understanding of non-Markovian quantum dynamics.

Contribution

It provides one of the few exactly solvable models for infinite-dimensional quantum systems with non-Markovian effects.

Findings

Derived the Green's function for the model

Analyzed Gaussian wave function evolution with exponential noise correlation

Established a new benchmark for non-Markovian quantum dynamics

Abstract

We provide the exact analytic solution of the stochastic Schr\"odinger equation describing an harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models, for infinite dimensional systems. We compute the Green's function; in the case of a free particle, and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.