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Chinese Physics Letters

Fluctuation of Mesoscopic RLC Circuit at Finite Temperature

Zhang Xiao-Yan, Ji‐Suo Wang, Fan Hong-Yi

Published Sep 1, 2008• 9 citations
Publisher

Abstract

We consider the fluctuation of mesoscopic RLC circuit at finite temperature since a resistance always produces Joule heat when the circuit is working. By virtue of the thermo Geld dynamics and the coherent thermo state representation we show that the quantum mechanical zero-point fluctuations of both charge and current increase with the rising temperature and the resistance value.

DOI
10.1088/0256-307x/25/9/009

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We consider the fluctuation of mesoscopic RLC circuit at finite temperature since a resistance always produces Joule heat when the circuit is working. By virtue of the thermo Geld dynamics and the coherent thermo state representation we show that the quantum mechanical zero-point fluctuations of both charge and current increase with the rising temperature and the resistance value.
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.