The quantization scheme of the nondissipative mesoscopic active LC circuit is proposed by introducing the normal variable depending on current or voltage, the quantum fluctuations of current and voltage in the eigenstate of the circuit are investigated, the results are analyzed and discussed.
Starting with the equation for the classical motion of nondissipative mesoscopic mutual inductance coupled circuits, we studied the quantization scheme of the coupled circuits and the quantum fluctuation of the voltage and current in the eigenstate of the coupled circuits. The results show that the quantum fluctuation in each circuit is related not only to itself elements and the eigenstate of the coupled circuits ,but also to another circuit elements and the mutual inductance coefficients of the coupled circuits.
A mesoscopic parallel LC circuit model with double dissipative branch circuits is put forward according to the actual situation of the circuit.It is quantized with the theory of the classical circuit and the quantization method of damped harmonic oscillator.Then the quantum fluctuations of the voltage and the current of the circuit in vacuum state and the quantum fluctuations affected by the dissipative resistances are discussed.The results show that the quantum fluctuations of the voltage and the current of both branches are not only related with the parameters of the LC circuit components,but also affected by the dissipative resistances.They decay with the same exponential with time.The coefficients of the quantum fluctuations of the current are the same,while those of the voltage are different.When the two dissipative resistances are equal,the quantum fluctuations of the voltage and the current of both branches take on the same behavior respectively.