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Acta Physica Sinica

Quantum effect of dissipative mesoscopic capacitance coupled circuit

Qiu Shen-Yu, Cai Shao-Hong, (1)贵州大学物理系，贵阳 550025; (2)贵州大学物理系，贵阳 550025;贵阳财经学院，贵阳 550004

Published Jan 1, 2006• 5 citations
Publisher

Abstract

The dissipative mesoscopic coupled circuits are obtained by the method of damped harmonic oscillator quantization . The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given .The result shows that the quantum fluctuations of the charge and current exist in all states, and the fluctuations in the component circuits are corelated.

DOI
10.7498/aps.55.816

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The dissipative mesoscopic coupled circuits are obtained by the method of damped harmonic oscillator quantization . The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given .The result shows that the quantum fluctuations of the charge and current exist in all states, and the fluctuations in the component circuits are corelated.
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.
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.
The effects of the difference of circuit parameters or capacitances and inductances on the quantum fluctuations in the non-resonant damped mesoscopic coupled electric circuits were studied. In the calculations, the physical mechanism of the generation of the resistance or the interaction between electrons and phonons was considered. The difference of the circuit parameters in the two component circuits makes the quantum fluctuations in one component circuit smaller and that in the other larger. The results also show that both capacitance coupling and inductance coupling will cause the quantum fluctuations of the electric charge in the coupling part squeezed. But there is no squeezing for the electric current in the coupling part.
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.