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Chinese Physics

Quantum fluctuations of mesoscopic damped double resonance RLC circuit with mutual capacitance–inductance coupling in thermal excitation state

Xing-Lei Xu, Hongqi Li, Ji‐Suo Wang

Published Aug 1, 2007• 15 citations
Publisher

Abstract

Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics (TFD), the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling is proposed. The quantum fluctuations of charge and current of each loop in a squeezed vacuum state are studied in the thermal excitation case. It is shown that the fluctuations not only depend on circuit inherent parameters, but also rely on excitation quantum number and squeezing parameter. Moreover, due to the finite environmental temperature and damped resistance, the fluctuations increase with the temperature rising, and decay with time.

DOI
10.1088/1009-1963/16/8/051

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Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics (TFD), the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling is proposed. The quantum fluctuations of charge and current of each loop in a squeezed vacuum state are studied in the thermal excitation case. It is shown that the fluctuations not only depend on circuit inherent parameters, but also rely on excitation quantum number and squeezing parameter. Moreover, due to the finite environmental temperature and damped resistance, the fluctuations increase with the temperature rising, and decay with time.
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Mesoscopic double resonance mutual inductance and capacitance coupling circuit is quantized by the method of harmonic oscillator quantization linear transformation.The energy spectra of this circuit are given.The quantum fluctuations of the charge and current of each loop are researched by the method of thermo-field dynamics(TFD) in thermal excited state,thermal squeezed vacuum state,thermal vacuum state and vacuum state.It is show that,the quantum fluctuations of the charge and current are related to not only circuit inherent parameter and coupled magnitude,but also quantum number of excitation,squeezed coefficients,squeezed angle,environmental temperature.And,the quantum fluctuations increase with the increase of temperature.
A mesoscopic double resonance circuit with mutual inductance and capacitance-inductance coupling was quantized using canonical quantization method.The Hamiltonian of the system was diagonalized by unitary transformation to obtain the eigenenergy spectra of the circuit.The quantum fluctuations of the charge and current in the two loops of the circuit were studied under squeezed vacuum excitation state,squeezed vacuum state and vacuum state,respectively.The results show that quantum fluctuations are dependent not only on circuit parameters,quantum number of excitation,squeezed coefficients and squeezed angle,but also on mutual inductance coefficient,capacitance and inductance.
When the inelastic coherence length of the charge carrier reaches the Fermi wavelength,quantum effects in electronic devices and circuit should be taken into account.Due to the existence of finite environmental temperature and damped resistance,practical circuits are always working in damped thermal states at finite temperature.With the rapid development of nanotechnology and microeletronics,the quantum effects of mesoscopic circuit have become an active problem now.In this paper,mesoscopic series-parallel connection RLC circuit was quantized by the method of damped harmonic oscillator quantization.Quantum fluctuatioins of the current and voltage of each branch were studied by thermo-field dynamics(TFD) theory in thermal vacuum state,thermal coherent state and thermal squeezed state.The results show that the quantum fluctuations of the current and voltage of each branch are related to not only parameters of the circuit,but also squeezed coeficients,squeezed angle and envionmental temperature.Because of the existence of current Joule heat,environmental temperature and damped resistances,the fluctuations increase with the increasing of temperature and decay with time.The study of these quantum fluctuation is significant for the design of miniature circuits and the reduction of quantum noise.