Quantum Dynamics of a Resonator Coupled to a SET

We study the quantum dynamics of a resonator driven by a superconducting single-electron transistor. We prove the existence of the Minimal Quantum Dynamical Semigroup \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {T}^{\,({\rm min})}}$$\end{document} solving the evolution equation for the density matrix, then we prove that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {T}^{\,({\rm min})}}$$\end{document} is Markov. Moreover we prove the existence and uniqueness of a faithful normal stationary state and show that the dynamics converges towards this stationary state when time goes to infinity.