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Modern Physics Letters B

FLUCTUATION OF MESOSCOPIC RLC CIRCUIT AT PHOTON-SUBTRACTED AND PHOTON-ADDED THERMO VACUUM STATES WITH FINITE TEMPERATURE

Xue-xiang Xu, Liyun Hu, Hong-Yi Fan

Published Dec 6, 2010• 4 citations
Publisher

Abstract

By using the Wigner function to evaluate expectation values of any symmetrically order of operator in a classical fashion, we study the quantum fluctuation and the uncertainty relation of mesoscopic RLC circuit at photon-subtracted and photon-added thermo vacuum states. It is found that the fluctuations and the uncertainty relation of both charge and current are linearly related to the photon-subtracted and photon-added number.

DOI
10.1142/s021798491102547x

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By using the Wigner function to evaluate expectation values of any symmetrically order of operator in a classical fashion, we study the quantum fluctuation and the uncertainty relation of mesoscopic RLC circuit at photon-subtracted and photon-added thermo vacuum states. It is found that the fluctuations and the uncertainty relation of both charge and current are linearly related to the photon-subtracted and photon-added number.
By using the partial trace method and the technique of integration within an ordered product of operators we obtain the explicit expression of the generalized thermal vacuum state (GTVS) for an RLC circuit instead of using the Takahashi–Umezawa approach. According to thermal field dynamics (TFD), namely, the expectation value of physical observables in this GTVS is equivalent to their ensemble average, based on GTVS we successfully derive the quantum fluctuations at nonzero temperature and the thermodynamical relations for the mesoscopic RLC circuit. Our results show that the higher the temperature is, the more quantum noise the RLC circuit exhibits.
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.
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.