Started from the classical equation of an active RLC circuit, after t he quantization of an active RLC circuit, we calculated the quantum fluctuation of the current and the charge in the mesoscopic RLC circuit, and we also studied the influence of source on quant um fluctuation.
To investigate the factors influencing quantum fluctuations,the quantum fluctuations of charge,current and energy in a mesoscopic RLC circuit were calculated in a new Fock space defined by the charge operator using the character of the minimum shift operator based on charge quantization. The results show that,taking account of charge discreteness,the quantum fluctuation of current is zero under the eigenstate of ladder operator,and the fluctuations of charge and energy are determined by charge quantum,Planck constant and state parameters. In addition,the fluctuation of energy depends also on RLC parameters of the circuit,the power source and the external magnetic field.
Starting from equation of motion of the active RLC circuit, we adopt the technique of the unitary transformation,transform the charge and current into the unitary variable and then have them quantization. By making use of standard transformation, we try to solve the having time Schrdinger equation. As the application, quantum fluctuations and antibunching effect of the charge and the current in the mesoscopic circuit in the harmonic oscillator state is studied, the result is analysed and discussed.