Feshbach projection formalism for open quantum systems

TL;DR

This paper introduces a novel Feshbach projection-based method for open quantum systems, allowing for consistent approximations and the construction of valid quantum evolutions, demonstrated on the spin-boson model.

Contribution

It develops a new formalism for open quantum systems using Feshbach projections, improving approximation consistency over traditional methods.

Findings

Enables construction of legitimate quantum evolutions

Allows consistent approximations in open quantum systems

Successfully applied to spin-boson model beyond RWA

Abstract

We provide a new approach to open quantum systems which is based on the Feshbach projection method in an appropriate Hilbert space. Instead of looking for a master equation for the dynamical map acting in the space of density operators we provide the corresponding equation for the evolution in the Hilbert space of the system. Its solution enables one to construct a legitimate quantum evolution (completely positive and trace preserving). The big advantage of this approach is the ability of performing a consistent approximation which creates notorious problems in the standard Nakajima-Zwanzig approach. The new scheme is illustrated by well known spin-boson model beyond rotating wave approximation.