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.