Investigation of synchronization for coupled quantum nonlinear electrical LC circuits with mutual inductance

The quantum Hamiltonian operator is found for a pair of nonlinear electrical LC circuit consisting of nonlinear capacitors and linear inductors for mutually coupled inductance. The effect of mutual inductance on zero-point energy has been investigated with analytical and numerical approaches. In the rotating-wave approximation, by introducing continuous variables of electric charge and current operators and defining quadrature operators as synchronization errors, quantum fluctuations were obtained as a function of the characteristic parameters. The effect of the mutual inductance on time-dependent synchronization for the squeezed states has been investigated with a numerical approach and is indicated that the two nonlinear circuits are synchronized.