Semiclassical theory of decoherence in mesoscopic dissipative circuit

We present a quantum theory of decoherence for a mesoscopic dissipative circuit. Using Kirchhoff laws of classical circuit and quantum theory, a Hamitonian of the circuit is derived. The dissipative circuit elements (external impedance, shunt resistors) are described using the Caldeira–Leggett model. The master equation for the dissipative circuit in the Born–Markov approximation is derived and brought into the well-known Bloch–Redfield formalism. Then, we study decoherence properties of multilevel dissipative quantum circuit. At a very low temperature, energy relaxation time and decoherence time of the circuit are give when adopting two-level state approximation.