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Chinese Journal of Quantum Electronics

Quantum fluctuations of current in a mesoscopic lossless transmission line at finite temperature

AN Guang-lei

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

By making use of thermo-field dynamics (TFD), the quantum fluctuations of current of the mesoscopic lossless transmission line in the vacuum state, the coherent states and the squeezed states with thermal noise have been studied. Thus the dependence of the fluctuations on temperature in these states at finite temperature can be seen. It is shown that the quantum fluctuations depend on not only the parameters of the transmission line but also the environmental temperature T. The higher the temperature, the more quantum noise the line exhibits.

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By making use of thermo-field dynamics (TFD), the quantum fluctuations of current of the mesoscopic lossless transmission line in the vacuum state, the coherent states and the squeezed states with thermal noise have been studied. Thus the dependence of the fluctuations on temperature in these states at finite temperature can be seen. It is shown that the quantum fluctuations depend on not only the parameters of the transmission line but also the environmental temperature T. The higher the temperature, the more quantum noise the line exhibits.
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.
In this paper we consider a non-dissipative distributed parameter circuit at a finite temperature T. We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation. Thermal field dynamic is used in our discussion. It is shown that distributing parameter circuits and quantum fluctuations, which also have distributing properties, are related to both the circuit parameters and the positions and the model of signals and temperature T. The higher the temperature, the more quantum noise the circuit exhibits. The research will be helpful to miniaturize intergreate circuits and electric components. It will be also significant for the futher study of the qualitities of mesoscopic system.