Starting from the Hamilton which is given by the coupling both of charge and current in the non-dissipative mesoscopic capacitance and inductance coupling circuit,the method of quantization in the circuit is obtained,and based on it we also discussed two particular situations.
Starting from the classical movement equation of a non-dissipative inductance coupled mesoscopic circuit,the circuit is quantized by using linear transformation method,and the quantum fluctuations of currents and charges at excited coherent states are calculated.The results show that the average and square average of current and charge of each loop are not zero without power,i.e.,there exist quantum fluctuations. And the fluctuations are not only determined by the loop parameters,but also related to another loop's parameters and coupled inductance parameters.The quantum fluctuations in two circuits are relevant,and obviously depend on the state parameters of circuits,i.e.,parameters of particle count states and coherent states.