概マシュー作用素
出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2014/08/04 21:59 UTC 版)
数理物理学の分野における概マシュー作用素（がいマシューさようそ、英: almost Mathieu operator）とは、量子ホール効果の研究に現れる、次のような作用素のことを言う。
- ^ Simon, Barry (2000). “Schrödinger operators in the twenty-first century”. Mathematical Physics 2000. London: Imp. Coll. Press. pp. 283–288. ISBN 186094230X.
- ^ Avila, A. (2008). “The absolutely continuous spectrum of the almost Mathieu operator”. Preprint. arXiv:0810.2965.
- ^ Gordon, A. Y.; Jitomirskaya, S.; Last, Y.; Simon, B. (1997). “Duality and singular continuous spectrum in the almost Mathieu equation”. Acta Math. 178 (2): 169–183. doi:10.1007/BF02392693.
- ^ Jitomirskaya, Svetlana Ya. (1999). “Metal-insulator transition for the almost Mathieu operator”. Ann. of Math. 150 (3): 1159–1175. JSTOR 121066.
- ^ Avron, J.; Simon, B. (1982). “Singular continuous spectrum for a class of almost periodic Jacobi matrices”. Bull. Amer. Math. Soc. 6 (1): 81–85. Zbl 0491.47014.
- ^ Jitomirskaya, S.; Simon, B. (1994). “Operators with singular continuous spectrum, III. Almost periodic Schrödinger operators”. Comm. Math. Phys. 165 (1): 201–205. Zbl 0830.34074.
- ^ Last, Y.; Simon, B. (1999). “Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators”. Invent. Math. 135 (2): 329–367. doi:10.1007/s002220050288.
- ^ Bourgain, J.; Jitomirskaya, S. (2002). “Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential”. Journal of Statistical Physics 108 (5–6): 1203–1218. doi:10.1023/A:1019751801035.
- ^ Avila, A.; Jitomirskaya, S. (2005). “The Ten Martini problem”. Preprint. arXiv:math/0503363.
- ^ Bellissard, J.; Simon, B. (1982). “Cantor spectrum for the almost Mathieu equation”. J. Funct. Anal. 48 (3): 408–419. doi:10.1016/0022-1236(82)90094-5.
- ^ Puig, Joaquim (2004). “Cantor spectrum for the almost Mathieu operator”. Comm. Math. Phys. 244 (2): 297–309. doi:10.1007/s00220-003-0977-3.
- ^ Avila, A.; Krikorian, R. (2006). “Reducibility or non-uniform hyperbolicity for quasiperiodic Schrödinger cocycles”. Annals of Mathematics 164 (3): 911–940. doi:10.4007/annals.2006.164.911.
[続きの解説]
「概マシュー作用素」の続きの解説一覧
- 1 概マシュー作用素とは
- 2 概マシュー作用素の概要
- 概マシュー作用素のページへのリンク
