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

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.