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College Physics

The application of Wigner function in mesoscopic LC circuit at finite temperature

Yuqian Zhang

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

The marginal distribution of Winger function in mesoscopic LC circuit at a finite temperature is in vestigated by means of the Wigner function. The results show that the marginal distributions statistical average for p2/ 2L and q2/ 2C of the Wigner function are exactly the energy stored in inductance and capacity of the mesoscopic LC circuit,respectively at finite temperature.

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The marginal distribution of Winger function in mesoscopic LC circuit at a finite temperature is in vestigated by means of the Wigner function. The results show that the marginal distributions statistical average for p2/ 2L and q2/ 2C of the Wigner function are exactly the energy stored in inductance and capacity of the mesoscopic LC circuit,respectively at finite temperature.
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 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.
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.