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Chinese Journal of Quantum Electronics

Quantum fluctuations of mesoscopic LC circuit at finite temperature

Qi-Liang He

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

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.

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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 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.
By extending the thermal field dynamics to the time dependent system, quantum fluctuations of the time dependent mesoscopic LC electric circuit at finite temperature were studied. While the up going temperature will increase the quantum fluctuations, time changes of the physical quantities such as the inductance and capacitance can suppress the quantum fluctuations. The electric source will not affect the quantum fluctuations, but will contribute to the averages of the charge and magnetic flux. It was also found that if there is a source, the averages will depend on the temperature; if there is no source, the averages will be zero and so temperature independent.
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.