Quantum effects of the mesoscopic LC electric circuit in thermal Kerr state

Based on the fact that a mesoscopic capacitor can be regarded as a mesoscopic tunnel junction, we quantized the mesoscopic LC circuit by using the rotating-wave approximation. The study shows: Considering the coupled energy of the mesoscopic capacitor, the system of the mesoscopic LC circuit will be equivalent to a Kerr system. We also used the thermal field dynamic theory to investigate the thermal Kerr state at a definite temperature and calculated the quantum fluctuation of both charge and magnetic flux, and discussed the results.