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Chinese Physics B

Thermal effect and energy-level transition rule for a mesoscopic LC circuit with inductance–capacitance coupling

Jie Su, Ji‐Suo Wang, Liang Bao-Long, Zhang Xiao-Yan

Published May 1, 2009• 2 citations
Publisher

Abstract

This paper reports that the mesoscopic inductance and capacitance coupling LC circuit is quantized by means of the canonical quantization method. Using the 'invariant eigen-operator' method, it deduces the energy-level transition rule when the system is disturbed by an external electromagnetic field. At the same time, the quantum fluctuations for the system at finite temperature are examined by virtue of the generalized Hellmann–Feynman theorem.

DOI
10.1088/1674-1056/18/5/049

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This paper reports that the mesoscopic inductance and capacitance coupling LC circuit is quantized by means of the canonical quantization method. Using the 'invariant eigen-operator' method, it deduces the energy-level transition rule when the system is disturbed by an external electromagnetic field. At the same time, the quantum fluctuations for the system at finite temperature are examined by virtue of the generalized Hellmann–Feynman theorem.
Using the Lagrangian function,the Hamiltonian of the inductance coupling mesoscopic circuits is given.The Hamiltonian operator is diagonalized by introducing a unitary operator.By virtue of the generalized Hellmann-Feynman theorem,the quantum fluctuations of charge and its conjugate quantity for the system at finite temperature are investigated.It is found that,the quantum fluctuations of charge and its conjugate quantity have something to do with not only the parameters of the citcuit cells,but also the temperature.
By extending the thermal field dynamics to the time dependent system, quantum fluctuations of the time dependent mesoscopic LC electric circuit at finite temperature were studied. While the up going temperature will increase the quantum fluctuations, time changes of the physical quantities such as the inductance and capacitance can suppress the quantum fluctuations. The electric source will not affect the quantum fluctuations, but will contribute to the averages of the charge and magnetic flux. It was also found that if there is a source, the averages will depend on the temperature; if there is no source, the averages will be zero and so temperature independent.