A method of quantizing the active parallel mesoscopic RLC circuits developed,and the quantum fluctuations of currents and voltages in the parallel mesoscopic RLC circuits in the vacuum state,especially the influences of resistance on the quantum fluctuation are investigted.
The quantization of the generalized mesoscopic RLC parallel circuit,the quantum fluctuations of the current and the voltage of each branch in vacuum state were studied.The influences on the quantum fluctuations of the dissipative resistances in the inductance and capacitance branches were discussed.The results show that the quantum fluctuations in each branch are related to the parameters of the elements and decay with time.The quantum fluctuations in the two branches are influenced by the dissipative resistances both in the decaying factor and in the coefficients.They have the same behavior in the decaying factor but having difference in the coefficients.The quantum fluctuations of the voltage are affected by the dissipative resistances in the two branches,but the quantum fluctuations of the current are not affected by them when the values of the two dissipative resistances are same.
By referring to the idea of dealing with damped harmonic oscillator in quantum mechanics,the mesoscopic parallel RLC circuit with dissipative capacitance branch circuit is quantized.On this basis,the quantum fluctuations of the voltage and current of each branch circuit in vacuum state are studied.The result shows that the quantum fluctuations of the voltage and current of each branch circuit are related with the parameters of the circuit elements,and decay according to exponent along with time,and that the attenuations of the quantum fluctuations are the same,but their coefficients are different,and that the quantum fluctuations of the voltage and current of each branch circuit are affected by the dissipative resistance.