A method of quantizing an active RLC circuit is developed, and the quantum fluctuations of the charge and current in the mesoscopic RLC circuit in the squeezed vacuum state, especially the influences of the resistance and the squeezing parameters on the quantum fluctuations are investigated.
The quantum fluctuations of the voltage and the current in each branch of the quantized generalized mesoscopic RLC parallel circuit in squeezed vacuum state were studied.The factors affecting the fluctuations in each branch were also analyzed.The results show that the quantum fluctuations in each branch of the circuit in squeezed vacuum state are related to the factors which are the elements of the circuit,the parameters of the squeezed vacuum state and the time.All the quantum fluctuations of the voltage and the current in each branch of the circuit decay with time exponentially.The decay rates are related to the elements of the circuit only,not to the parameters of the squeezed vacuum state.The amplitude of the fluctuations at the initial stage depends on the elements of the circuit and the parameters of the squeezed vacuum state.
Mesoscopic series-parallel connection RLC circuit is quantized by the method of damped harmonic oscillator operation.On this basic theory,quantum fluctuations of the current and voltage of each branch in excitation state of the squeezed vacuum state,squeezed vacuum state and vacuum state are studied.The result shows that the quantum fluctuations of the current and voltage of each branch are related with not only parameter of the circuit element,but also quantum number of excitation,squeezed coefficients and squeezed angle.These fluctuations decay with time because of damped resistance.