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Chinese Journal of Quantum Electronics

Quantization of mesoscopic RLC circuit and its quantum effects at finite temperature

Ji‐Suo Wang

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

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.

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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.
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.
By using canonical quantization method of damped harmonic oscillator,the quantum of dissipative mesoscopic RLC series and parallel circuit was realized in this paper.And on this basis,the quantum fluctuations of charge and inductance flux linkage as the same as voltage and current in circuit under thermal vacuum state which based on thermal field dynamics theory were also studied through this research methods.The results show that charge and inductance flux linkage as the same as voltage and current in circuit under thermal vacuum state respectively exist quantum fluctuations.And the quantum fluctuations and quantum fluctuations plot not only depend on device parameters in the circuit,but also depend on time and temperature.
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 the quantum canonic ensemble theory,the density matrix and the Wehrl entropy of a harmonic oscillator are derived in a thermal field.The mesoscopic RLC series circuit is equivalent to a harmonic oscillator.The relation between the Wehrl entropy and the quantum effects of mesoscopic circuit is proposed at a finite temperature.It is shown that the Wehrl entropy of a harmonic oscillator not only depends on the eigenfrequency,but also relies on the temperature.The quantum fluctuations of charge,magnetic flux and the corresponding uncertainty relation increase monotonously with the Wehrl entropy,thereby increase monotonously with the temperature,and consistent with results of the thermal field dynamics(TFD).So the Wehrl entropy can be regarded as a measurement of the quantum effects of the mesoscopic circuit.
By using the information-theoretic Wehrl entropy,the Wehrl entropy of a harmonic oscillator is obtained in thermal field.The mesoscopic RLC electric circuit is quantized.The relation between the Wehrl entropy and the quantum effects of mesoscopic RLC electric circuit is researched in thermal field.These results show that the Wehrl entropy is related to not only the engenfrequency,but also the temperature.And the quantum fluctuation and the corresponding uncertainty relation of charge and magnetic flux grow with the Wehrl entropy increasing and become small with the Wehrl entropy decreasing.So the Wehrl entropy can be regarded as a best measurement of the quantum fluctuation and the corresponding uncertainty of mesoscopic RLC electric circuit.