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Chinese Physics

Quantum fluctuations in mesoscopic resistance- inducatance-capacitance electric circuits at finite temperature

Xian-Ting Liang, Fan Hong-Yi

Published Jun 1, 2001• 14 citations
Publisher

Abstract

By using the charge and current in a quantization resistance-inductance-capacitance (RLC) electric circuit, we construct a pair of canonical variables. Using this pair of variables and the thermal field dynamics, we obtain the fluctuations of charge and current in the RLC electric circuit at finite temperatures. It is shown that the fluctuations increase with increasing temperature and decrease with prolonging of time.

DOI
10.1088/1009-1963/10/6/304

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By using the charge and current in a quantization resistance-inductance-capacitance (RLC) electric circuit, we construct a pair of canonical variables. Using this pair of variables and the thermal field dynamics, we obtain the fluctuations of charge and current in the RLC electric circuit at finite temperatures. It is shown that the fluctuations increase with increasing temperature and decrease with prolonging of time.
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 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.
The quantum wavefunctions and the corresponding energy levels of a RLC (Resistance-Inductance-Capacity) electric circuit are obtained by using canonical quantization method and unitary transformation from the classical equation of motion. The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given as well as the uncertainty relation. It is showed that even if at 0 K charge and current in the circuit exhibit quantum fluctuations, which originates from fluctuations of zero point vibrations of the system.
Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics (TFD), the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling is proposed. The quantum fluctuations of charge and current of each loop in a squeezed vacuum state are studied in the thermal excitation case. It is shown that the fluctuations not only depend on circuit inherent parameters, but also rely on excitation quantum number and squeezing parameter. Moreover, due to the finite environmental temperature and damped resistance, the fluctuations increase with the temperature rising, and decay with time.
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.