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ACTA PHOTONICA SINICA

Wigner Function of Mesoscopic Circuit by Virtue of the Thermo Tield Dynamics

张晓燕 ZHANG Xiao-yan, 王继锁 WANG Ji-suo

Published Jan 1, 2012• 1 citation
Publisher

Abstract

By virtue of the thermo field dynamics and the coherent thermo state representation,the Wigner function of mesoscopic RLC circuit at finite temperature was obtained,and the quantum fluctuations of mesoscopic RLC circuit at finite temperature were studied.By means of the Weyl correspondence and Wigner theorem the marginal distribution of Wigner function in mesoscopic RLC circuit was discussed.The physical meaning of marginal distributions′ statistical average of the Wigner function was explained.The results show that the quantum fluctuations of both charge and current of mesoscopic RLC circuit at finite temperature increase with the rising of temperature and resistance value,and the mesoscopic RLC circuit has squeezed effects between charge and current,caused by the quantum mechanical zero-point fluctuations;the marginal distributions′ statistical averages of the Wigner function are the energy stored in capacity and in inductance of the mesoscopic RLC circuit,respectively.

DOI
10.3788/gzxb20124104.0493

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By virtue of the thermo field dynamics and the coherent thermo state representation,the Wigner function of mesoscopic RLC circuit at finite temperature was obtained,and the quantum fluctuations of mesoscopic RLC circuit at finite temperature were studied.By means of the Weyl correspondence and Wigner theorem the marginal distribution of Wigner function in mesoscopic RLC circuit was discussed.The physical meaning of marginal distributions′ statistical average of the Wigner function was explained.The results show that the quantum fluctuations of both charge and current of mesoscopic RLC circuit at finite temperature increase with the rising of temperature and resistance value,and the mesoscopic RLC circuit has squeezed effects between charge and current,caused by the quantum mechanical zero-point fluctuations;the marginal distributions′ statistical averages of the Wigner function are the energy stored in capacity and in inductance of the mesoscopic RLC circuit,respectively.
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.
By using canonical transformation,the quantization scheme of mesoscopic RLC circuit is given.With the aid of numerical calculation,the regulation is investigated about how the Wigner function of the thermal vacuum state varies with the temperature.Meanwhile, the quantum effects of the charge and self-conductance magnetic flux in the thermal vacuum state are discussed by using Weyl-Wigner correspondence.It is found that,Wigner function of the thermal vacuum state at low temperature is a stable wave packet,but it diffuses with the temperature increasing and the quantum effects of charge and self-conductance magnetic flux in the thermal vacuum state vary with the temperature and time,besides the circuit parameters.
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.