Quantum Dynamics of a Resonator Coupled to a SET

Abstract

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 \({\mathcal {T}^{\,({\rm min})}}\) solving the evolution equation for the density matrix, then we prove that \({\mathcal {T}^{\,({\rm min})}}\) 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.