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Journal of Hebei Normal University

Quantum Canonic Ensemble Theory for Quantum Effects of Mesoscopic Circuit

Yushan Li

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

By using of the quantum canonic ensemble theory,the quantum effects of mesoscopic RLC series circuit have been studied in the energy mixed eigenstates.The relation between the quantum effects of mesoscopic circuit and the temperature has been obtained.The results show that the quantum fluctuations of mesoscopic RLC series circuit are not only related to engenfrequency of the circuit,but also the temperature.The quantum noise grows up with the temperature.This result agrees with that obtained by thermal field dynamics(TFD) .However the quantum canonic ensemble theory is easily understood and applied.

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By using of the quantum canonic ensemble theory,the quantum effects of mesoscopic RLC series circuit have been studied in the energy mixed eigenstates.The relation between the quantum effects of mesoscopic circuit and the temperature has been obtained.The results show that the quantum fluctuations of mesoscopic RLC series circuit are not only related to engenfrequency of the circuit,but also the temperature.The quantum noise grows up with the temperature.This result agrees with that obtained by thermal field dynamics(TFD) .However the quantum canonic ensemble theory is easily understood and applied.
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At a definite temperature,a mesoscopic circuit isn't in a determinate quantum state,but in the mixed state.Using the quantum canonic ensemble theory,the quantum fluctuations of charge and circuit of a mesoscopic LC circuit in the mixed state were studied. It is shown that the quantum fluctuations of a mesoscopic LC circuit depend on not only the circuit component parameters,but also the temperature.The higher the temperature,the more quantum noise the mesoscopic LC exhibits.This method is more easily understood and applied than the TFD method.As the mesoscopic circuit is always at finite temperatures,the result is useful for controlling the quantum fluctuations of 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.
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.
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.