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Journal of Southwest Jiaotong University

Quantum Fluctuations in Damped Inductive-Coupled Electric Circuit

Liang Mai-lin

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
Mesoscopic damped mutual inductance coupled double resonance RLC circuit is quantized by the method of damped harmonic oscillator quantization and linear transformation. The energy levels of this circuit are given. By thermo-field dynamics (TFD), the quantum fluctuations of the current and voltage of each loop are researched in the thermal vacuum state, thermal coherent state and thermal squeezed state. It is shown that the quantum fluctuations of the current and voltage are related not only to the circuit inherent parameter and coupled magnitude of mutual inductance, but also squeezed coefficients, squeezed angle, environmental temperature and damped resistance. Furthermore, because of environmental temperature and damped resistance, the quantum fluctuations increase with the increase of temperature and decay along with time.