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.

10 pages, 3 figures, submitted to J. Phys. A

References in corpus (8)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Super-fermion representation of the Lindblad master equation for the electron transport problem
• Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems
• Noise-driven quantum criticality
• Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems