摘要The generalized Lagrangian is defined in a dissipative electromagnetic medium on the basis of the combination of dynamical analysis and fractional derivative. Lorentz medium models are obtained by formulating relevant Euler--Lagrange equations. The invariance is obtained subsequently by investigating the invariance of time variation in the system, and then the relation between the related Hamiltonian and electromagnetic energy density is investigated. Canonical equations are obtained eventually. The electrodynamic interpretation on dissipative electromagnetic systems is revealed.
Abstract：The generalized Lagrangian is defined in a dissipative electromagnetic medium on the basis of the combination of dynamical analysis and fractional derivative. Lorentz medium models are obtained by formulating relevant Euler--Lagrange equations. The invariance is obtained subsequently by investigating the invariance of time variation in the system, and then the relation between the related Hamiltonian and electromagnetic energy density is investigated. Canonical equations are obtained eventually. The electrodynamic interpretation on dissipative electromagnetic systems is revealed.
收稿日期: 2006-09-30
出版日期: 2007-03-26
引用本文:
TAN Kang-Bo;LIANG Chang -Hong;DANG Xiao-Jie. Electrodynamic Analysis of Dissipative Electromagnetic Materials Based on Fractional Derivative[J]. 中国物理快报, 2007, 24(4): 847-850.
TAN Kang-Bo, LIANG Chang -Hong, DANG Xiao-Jie. Electrodynamic Analysis of Dissipative Electromagnetic Materials Based on Fractional Derivative. Chin. Phys. Lett., 2007, 24(4): 847-850.
[1] Bauer P S 1931 Proceedings of the National Academy ofSciences of USA 17 311 [2] Bateman H 1931 Phys. Rev. 38 815 [3] Caldirola P 1941 Nuovo Cimento 18 393 [4] Xu G O and Xu M J 2005 Chin. Phys. Lett. 22 1303 [5] Xu G O, Xu M J and Yang Y T 2005 Chin. Phys. Lett. 221573 [6] Ray J R 1979 Am. J. Phys. 47 626 [7] Englman R and Yahalom A 2003 Phys. Lett. A 314 367 [8] Loudon R 1970 J. Phys. A 3 233 [9] Ruppin R 2002 Phys. Lett. A 299 309 [10] Cui T J and Kong J A 2004 Phys. Rev. B 70 205106 [11] Riewe F 1996 Phys. Rev. E 53 1890 [12] Riewe F 1997 Phys. Rev. E 55 3581 [13] Miller K S and Ross B 1993 An Introduction to the FractionalCalculus and Fractional Differential Equations (New York: Wiley) [14] Landau L D, Lifshitz E M and Pitaevskii L P 1984 Electrodynamics of Continuous Media 2nd edn (Oxford: Pergamon) [15] Jackson J D 1999 Classical Electrodynamics 3rd edn (NewYork: Wiley) chap 6 [16] Smith D R and Kroll N 2000 Phys. Rev. Lett. 85 2933 [17] Shelby R A, Smith D R and Schultz S 2001 Science 29277 [18] Pendry J B and Smith D R 2004 Physics Today 57(2)37 [19] Grbic A and Eleftheriades G V 2004 Phys. Rev. Lett. 92117403 [20] Jiang H T, Chen H, Li H Q and Zhang Y W 2005 Chin. Phys.Lett. 22 884 [21] Quan B G, Li C, Sui Q, Li J J, Liu W M, Li Fang and Gu C Z 2005 Chin. Phys. Lett. 22 1243 [22] Goldstein H 1950 Classical Mechanics (Reading, MA: Addison-Wesley) [23] Broadbent C, Hovhammisyan G, Peatross J, Clayton M and Glasgow S2002 arXiv: physics/0207117 [24] Rosenberg R M 1977 Analytical Dynamics of Discrete Systems(New York: Plenum) chaps 10 and 16 [25] Meirovitch L 1970 Methods of Analytical Dynamics (New York:McGraw-Hill) chap 2
2007, Vol. 24 
