Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems

TL;DR

This paper introduces a stochastic projection method for modeling quantum dynamics in open systems with Bosonic or spin environments, leading to a new form of non-Markovian stochastic Schr"odinger equations that simplifies previous approaches.

Contribution

It develops a novel stochastic projection formalism for open quantum systems, providing a simplified non-Markovian stochastic Schr"odinger equation applicable to harmonic and spin environments.

Findings

Derives a new non-Markovian stochastic Schr"odinger equation without functional derivatives.

Extends the formalism to spin environments using spin coherent states.

Provides a unified approach for Bosonic and spin environment dynamics.

Abstract

We present a stochastic projection formalism for the description of quantum dynamics in Bosonic or spin environments. The Schr\"odinger equation in coherent state representation with respect to the environmental degrees of freedom can be reformulated by employing the Feshbach partitioning technique for open quantum systems based on the introduction of suitable non-Hermitian projection operators. In this picture the reduced state of the system can be obtained as a stochastic average over pure state trajectories. The corresponding non-Markovian stochastic Schr\"odinger equations include a memory integral over the past states. In the case of harmonic environments and linear coupling the approach gives a new form of the established non-Markovian quantum state diffusion (NMQSD) stochastic Schr\"odinger equation without functional derivatives. Utilizing spin coherent states, the evolution equation for spin environments resembles the Bosonic case with, however, a non-Gaussian average for the reduced density operator.