Extending third quantization with commuting observables: a dissipative spin-boson model

TL;DR

This paper extends third quantization to include commuting observables in a dissipative spin-boson model, providing a framework for analyzing open quantum systems with bosons and spins.

Contribution

It introduces a novel extension of third quantization for systems with commuting observables, applied to a dissipative spin-boson model.

Findings

Analyzed spectral and initial value problems for the master equation.

Worked out a detailed example of a single open spin-boson system.

Demonstrated the applicability of the extended framework to systems with spins and bosons.

Abstract

We consider the spectral and initial value problem for the Lindblad-Gorini-Kossakowski-Sudarshan master equation describing an open quantum system of bosons and spins, where the bosonic parts of the Hamiltonian and Lindblad jump operators are quadratic and linear respectively, while the spins couple to bosons via mutually commuting spin operators. Needless to say, the spin degrees of freedom can be replaced by any set of finite-level quantum systems. A simple, yet non-trivial example of a single open spin-boson model is worked out in some detail.