Abstract
For L-C circuit, a new quantized scheme has been proposed in the context of number-phase quantization. In this quantization scheme, the number n of the electric charge q(q=en) is quantized as the charge number operator and the phase difference θ across the capacity is quantized as phase operator. Based on the scheme of number-phase quantization and the thermo field dynamics (TFD), the quantum fluctuations of the charge number and phase difference of a mesoscopic L-C circuit in the thermal vacuum state, the thermal coherent state and the thermal squeezed state have been studied. It is shown that these quantum fluctuations of the charge number and phase difference are related to not only the parameters of circuit, the squeezing parameter, but also the temperature in these quantum states. It is proven that the number-phase quantization scheme is very useful to tackle with quantization of some mesoscopic electric circuits and the quantum effects.
Similar content being viewed by others
References
Louisell, W.H.: Quantum Statistical Properties of Radiation. Wiley, New York (1973)
Chen, B., et al.: Quantum effects in a mesoscopic circuit. Phys. Lett. A 205, 121–124 (1995)
Fan, H.Y., Liang, X.T.: Quantum fluctuation in thermal vaccuum state for mesoscopic LC electric circuit. Chin. Phys. Lett. 17, 174–176 (2000)
Wang, J.S., Liu, T.K., Zhan, M.S.: Quantum fluctuations of a mesoscopic capacitance coupling circuits in a displaced squeezed Fock state. Acta Phys. Sinica 49, 2271–2275 (2000)
Xu, X.L., Li, H.Q., Wang, J.S.: The quantum fluctuation of mesoscopic damped mutual capacitance coupled double resonance RLC circuit in excitation state of the squeezed vacuum state. Int. J. Theor. Phys. 45, 2231–2562 (2006)
Fan, H.Y., Yue, F., Song, T.Q.: Quantum theory of mesoscopic electric circuits in entangled state representation. Phys. Lett. A 305, 222–230 (2002)
Meng, X.G., et al.: Number-phase quantization and deriving energy-Level gap of two LC circuits with mutual-inductance. Chin. Phys. Lett. 25, 1025–1028 (2008)
Fan, H.Y., et al.: Number-phase quantization scheme for LC circuit and Josephson junction’s Cooper pairs. Chin. J. Quantum Electron. 24, 168–172 (2007). (In Chinese)
Takahashi, Y., Umezawa, H.: Thermo field dynamics. Collect. Phenom. 2, 55–80 (1975)
Liang, B.L., Wang, J.S., Fan, H.Y.: Marginal distributions of Wigner function in a mesoscopic L-C circuit at finite temperature and thermal Wigner operator. Int. J. Theor. Phys. 45, 2231–2562 (2007)
Vourdas, A.: Mesoscopic Josephson junctions in the presence of nonclassical electromagnetic fields. Phys. Rev. B 49, 12040–12046 (1994)
Fan, H.Y., et al.: Cooper-pair number phase Wigner function for the bosonic operator Josephson model. Phys. Lett. A 359, 580–586 (2006)
Fearn, H., Collett, M.J.: Representation of squeezed states with thermal noise. J. Mod. Opt. 35, 553–564 (1988)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, S. Number-Phase Quantization Scheme and the Quantum Effects of a Mesoscopic Electric Circuit at Finite Temperature. Int J Theor Phys 48, 1459–1465 (2009). https://doi.org/10.1007/s10773-008-9917-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-008-9917-5