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Acta Physica Sinica

Quantum fluctuations in the damped inductive-coupled electric circuit with resistances in the component circuits

Mai-Lin Liang, Yuan Bing, 天津大学理学院应用物理系，天津 300072

Published Jan 1, 2003• 5 citations
Publisher

Abstract

Using a new quantization idea of the damped electric circuit, the inductive-coupled electric circuit is quantized when there exist resistances in the component circuits. Quantum fluctuations are calculated and the temperature effects included.
DOI
10.7498/aps.52.978

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For the damped inductive coupled electric circuit with time-dependent inductances and capacitances,the system is quantized with the electron-phonon interaction included and the quantum fluctuations are calculated.In the studied coupled circuit,there are resistances both in the component circuits and in the coupling part.When the inductances and the capacitances are independent of time,the physical quantities will first decrease with oscillations and then reach a stable state.At the stable state,if the inductances and capacitances in the two component circuits are the same and the resistances go to zero,the quantum fluctuations will tend to that of the undamped circuit.
Based on the physical mechanism of the generation of resistance, i.e. the collision of electrons with lattices, the inductive-coupled electric circuit was quantized when there exists resistance in the coupling part. Quantum fluctuations were calculated for both the component circuits and the coupling part. And meanwhile, the temperature effect was included. The result shows that quantum fluctuations change with time, but reach definite values after a long time. The resistance in the coupling part affects the quantum fluctuations both in the coupling part and in the component circuits. Compared to the former results, the quantum fluctuations derived by this new method are smaller.
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.
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.