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Journal of Northeast Normal University

Quantum effect of mesoscopic dissipative parallel RLC circuit

Qiu Sheng-yu, Wenmei Li

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Mesoscopic dissipative parallel RLC circuit is quantized by the method of damped harmonic oscillator quantization.In the paper double-wave function quantum theory is applied to description of mesoscopic dissipative parallel RLC circuit with certain parameter and unitary phase,The quantum fluctuation of current and voltage are investigated,result of research show that the quantum fluctuation of mesoscopic dissipative parallel RLC circuit with unitary phase should be depicted in the theory of double-wave function.

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Mesoscopic dissipative parallel RLC circuit is quantized by the method of damped harmonic oscillator quantization.In the paper double-wave function quantum theory is applied to description of mesoscopic dissipative parallel RLC circuit with certain parameter and unitary phase,The quantum fluctuation of current and voltage are investigated,result of research show that the quantum fluctuation of mesoscopic dissipative parallel RLC circuit with unitary phase should be depicted in the theory of double-wave function.
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.
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.
In order to research quantum effect of a mesoscopic parallel circuit with mutual inductance coupled and damped, we adopt the method of damped harmonic oscillator quantization to quantize the circuit. By using unitary transform, the Hamiltonian of the system is diagonalized. Then we can get the energy levels of the circuit. Our results show that one such circuit can be equivalent to double module coupling harmonic oscillator, the quantum fluctuations of the electrical current and voltage not only relate to the parameters and mutual inductance coupling intensity of the circuit, but also to the quantum states of the circuit. And when the coupling intensity is colse to zero, the quantum fluctuations only relate to the inherence frequency of the circuit. Then we can control the quantum noises of the circuit by adjusting the parameters.
By using canonical quantization method of damped harmonic oscillator,the quantum of dissipative mesoscopic RLC series and parallel circuit was realized in this paper.And on this basis,the quantum fluctuations of charge and inductance flux linkage as the same as voltage and current in circuit under thermal vacuum state which based on thermal field dynamics theory were also studied through this research methods.The results show that charge and inductance flux linkage as the same as voltage and current in circuit under thermal vacuum state respectively exist quantum fluctuations.And the quantum fluctuations and quantum fluctuations plot not only depend on device parameters in the circuit,but also depend on time and temperature.