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Journal of Shanghai University (English Edition)

Non-Zero Temperature Evolution of the Quantum Fluctuations in Time-Dependent Inductive-Capacitive Coupled Circuit

Liang Mai

Published Jan 1, 2002• 0 citations
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Abstract

For time dependent inductive capacitive coupled circuits, the quantum fluctuations in the component circuits and the coupling part are computed. Generation of squeezing and the different effects of inductance and capacitance couplings on the quantum fluctuations are rigorously given. Meanwhile, the thermal effects are included.

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For time-dependent inductive-capacitive coupled circuits,the quantum fluctuations in the component circuits and the coupling part are computed.Generation of squeezing and the different effects of inductance and capacitance couplings on the quantum fluctuations are rigorously given,Meanwhile,the thermal effects are included.

Journal of Shanghai University (English Edition)•Jan 1, 2002•0 citations

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Nonzero Temperature Squeezing of the Time-Dependent Harmonic Oscillator and the Applications to the Capacitive Coupled Electric Circuit

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Communications in Theoretical Physics•May 15, 2002•5 citations
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.
Using the thermal field dynamics, the quantum fluctuations in the capacitive coupled electric circuits at finite temperature are calculated. At zero temperature, the eigenstates of the capacitive coupled electric circuit are the displaced Fock states. At finite temperature, the states become the thermal displaced Foek states. The results show that, in the coupling part of the circuit, which is not studied in former discussions, capacitance coupling reduces the quantum fluctuation of the electric charge and increase that of the electric current.