Semiclassical analysis and the magnetization of the hofstadter model

Physical Review Letters

Volumn 91, Issue 18, 2003, Pages

  Gat, O ^a   Avron, J E ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); ELECTRIC FIELDS; ELECTRON GAS; ELECTRONS; HAMILTONIANS; MAGNETIC FIELDS; MAGNETIC FLUX; MAGNETIZATION;

MIXED SYSTEMS; WAVE PACKETS;

QUANTUM THEORY;

EID: 18244416286     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.91.186801     Document Type: Article

References (33)

1. L.D. Landau and E.M. Lifshitz, Statistical Physics, edited by E.M. Lifshitz and L.P. Pitaevskii (Pergamon, Oxford, 1980), Pt.�1, 3rd ed.
2. R. Peierls, Z. Phys. 3, 1055 (1933);
3. P.G. Harper, Proc. Phys. Soc. London, Sect. A 68, 874–892 (1955).
4. W. Kohn, Phys. Rev. 115, 1460 (1959); 10.1103/PhysRev.115.1460
5. B.I. Blount, Phys. Rev. 126, 1636 (1962); 10.1103/PhysRev.126.1636
6. J. Zak, Phys. Rev. 168, 686 (1968); 10.1103/PhysRev.168.686
7. G. Nenciu, Rev. Mod. Phys. 63, 91 (1991).10.1103/RevModPhys.63.91
8. F. Axel, Beyond Quasicarystals (Springer, New York, 1995);
9. R.�Saito, G.�Dresselhaus, and M.�Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998).
10. M. Ya. Azbel, Sov. Phys. JETP 19, 634–645 (1964);
11. D. Hofstadter, Phys. Rev. B 14, 2239 (1976).10.1103/PhysRevB.14.2239
12. B. Helffer and J. Sjöstrand, Mem. Soc. Math. France 39, 1–139 (1989);
13. Y. Last, Commun. Math. Phys. 164, 421–432 (1994);
14. A.�Gordon, S.�Jitomirskaya, Y.�Last, and B.�Simon, Acta Math.ACMAA8 178, 169–183 (1997).
15. J. Bellissard, I. Guarneri, H. Schulz-Baldes, Commun. Math. Phys. 227, 515–539 (2002).10.1007/s002200200642
16. M. Wilkinson, J. Phys. AJPHAC5 20, 4337–4354 (1987); 10.1088/0305-4470/20/13/035
17. M.�Wilkinson, J. Phys. AJPHAC5 17, 3459–3476 (1984); 10.1088/0305-4470/17/18/016
18. R.�Ramal and J.�Bellissard, J. Phys. (Paris) 51, 1803–1830 (1990);
19. J.�Bellissard, C.�Kreft, and R.�Seiler, J. Phys. AJPHAC5 24, 2329–2353 (1991); 10.1088/0305-4470/24/10/019
20. B. Helffer and J. Sjöstrand, Mem. Soc. Math. France 40, 1 (1990).
21. R.G. Littlejohn and W.G. Flynn, Phys. Rev. A 44, 5239 (1991).10.1103/PhysRevA.44.5239
22. M.V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984).
23. C. Emmrich and A. Weinstein, Commun. Math. Phys. 176, 701–712 (1996);
24. J. Bolte and R. Glaser, math-ph/0204018.
25. G. Panati, H. Spohn, and S. Teufel, Phys. Rev. Lett. 88, 250405 (2002); 10.1103/PhysRevLett.88.250405
26. G. PanatiH. SpohnS. Teufelmath-ph/0212041;
27. G.�Sundaram and Q.�Niu, Phys. Rev. B 59, 14915 (1999); 10.1103/PhysRevB.59.14915
28. T.�Jungwirth, Q.�Niu, and A.H. MacDonald, Phys. Rev. Lett. 88, 207208 (2002).10.1103/PhysRevLett.88.207208
29. V.P. Maslov and M.V. Fedoryuk, Semiclassical Approximation in Quantum Mechanics (D. Reidel, Dordrecht, 1981).
30. J. Avron, R. Seiler, and B. Simon, Phys. Rev. Lett. 51, 51 (1983).10.1103/PhysRevLett.51.51
31. O. Gat and J. Avron, New J. Phys. 5, 44.1–44.8 (2003).
32. W. Chambers, Phys. Rev. 140, A135 (1965).
33. D.J. Thouless, M. Kohmoto, M.P. Nightingale, and M.�den�Nijs, Phys. Rev. Lett. 49, 405 (1982).10.1103/PhysRevLett.49.405