Quantum Fluctuations in a Damped Inductive Coupled Electric Circuit

According to the physical mechanism of the generation of resistance or the interaction of electrons with phonons, the inductive coupled electric circuit was quantized when there exist resistances in the component circuits. Relations of the quantum fluctuations in the component circuits and the coupling part with the parameters of the coupled circuit and the environmental temperature were given. Inductance coupling can reduce the quantum fluctuations of the electric currents, but will increase the quantum fluctuations of the electric charges. Similar to the electric circuit without resistance, electric sources affect the amount of the electric charge and current, but do not affect their quantum fluctuations. The former canonical quantization method, which starts from the classical equation of the electric charge and makes some transformations, this corresponds to applying the result of high temperature limit to the lower temperature case.