[1] [1] Buttiker M, Imry Y, Landauer R. Josephson behavior in small normal one-dimensional rings [J]. Phys. Lett. A, 1983, 96: 365.

[2] [2] Levy L P, et al. Magnetization of mesoscopic copper rings: Evidence for persistent currents [J]. Phys. Rev. Lett., 1990, 64: 2074.

[3] [3] Chandrasekhar V, et al. Magnetic response of a single isolated gold loop [J]. Phys. Rev. Lett., 1991, 67: 3578.

[6] [6] Louisell W H. Quantum Statistical Properties of Radiation [M]. New York: Wiley, NY 1973.

[7] [7] Gu Y J. Quantum fluctuations in a mesoscopic damped LC parallel electric circuit [J]. Chinese Physics, 2001, 10: 490.

[8] [8] Wang J S, Liu T K, Zhan M S. Entanglement swapping and disentanglement via an entangled state of atoms interacting with a cavity field [J]. Phys. Lett. A, 2002, 276: 155.

[11] [11] Fan H Y, Liang X T. Quantum fluctuation in thermo vacuum state for mesoscopic LC electric circuit [J]. Chin. Phys. Lett., 2000, 17: 174.

[13] [13] Ji Y H, Lei M S, Ouyang C Y. Shapiro effect in mesoscopic LC circuit [J]. Chinese Physics, 2002, 11: 163.

[14] [14] Liang X T, Fan H Y. Quantum fluctuations in mesoscopic resistance-inductance-capacitance electric circuits at finite temperature [J]. Chinese Physics, 2001, 10: 486-489.

[15] [15] Li Y Q, Chen B. Quantum theory for mesoscopic electric circuit [J]. Phys. Rev. B, 1996, 53: 4027.

[17] [17] Wan Huaming, et al. Evolution of quantum state for mesoscopic circuits with dissipation [J]. Communications in Theoretical Physics 2005, 44(6): 0253-6102.

[19] [19] Fan H Y. Representation and Transformation Theory in Quantum Mechanics [M]. Shanghai: Shanghai Scientific and Technical Press, 1997, 422 (in Chinese).