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Chinese Journal of Quantum Electronics

Quantization of the generalized mesoscopic RLC parallel circuit and its quantum fluctuations in vacuum state

YI Shi-guang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
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.