On the extended nature of edge states of Quantum Hall Hamiltonians

Annales Henri Poincare

Volumn 1, Issue 3, 2000, Pages 405-442

  Frohlich J ^a   Graf, G M ^a   Walcher, J ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034394014     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000230050001     Document Type: Article

References (29)

1. K. von Klitzing, G. Dorda, and N. Pepper, New method for high-accuracy determination of the fine structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45, 494 (1980)
2. R. B. Laughlin, Quantized Hall conductivity in two dimensions, Phys. Rev. B 23 5632-5633 (1981)
3. B. I. Halperin, Quantized Hall conductance, current-carrying edge states, ans the existence of extended states in a two-dimensional disordered potential, Phys. Rev. B 25, 2185-2190 (1982)
4. J. E. Avron and R. Seiler, Quantization of the Hall conductance for general, multiparticle Schrödinger Hamiltonians, Phys. Rev. Lett. 54, 259-262 (1985)
5. J. Fröhlich and T. Kerler, Universality in Quantum Hall systems, Nucl. Phys. B 354, 369 (1991)
6. X. G. Wen, Gapless boundary excitations in quantum Hall states and in the chiral spin states, Phys. Rev. B 43, 11025 (1991)
7. E. Mourre, Absence of singular continuous spectrum for certain self-adjoint operators, Commun. Math. Phys 78, 391-408 (1981)
8. P. Perry, I.M. Sigal, B. Simon, Spectral analysis of N-body Schrödinger operators, Ann. Math. 114, 519-567 (1981).
9. J. Sahbani, The conjugate operator method for locally regular Hamiltonians, J. Operator Theory 38, no. 2, 297-322 (1997)
10. 0-groups, commutator methods and spectral theory of N-body Hamiltonians, Progress in Mathematics, Birkhäuser 1996
11. V. Georgescu, C. Gérard, On the virial theroem in Quantum Mechanics, mp-arc 98-744 (1998)
12. M. Hübner and H. Spohn, Spectral properties of the spin-boson Hamiltonian, Ann. Inst. H. Poincaré Phys. Théor. 62, no.3, 289-323 (1995)
13. E. Skibsted, Spectral analysis of N-body systems coupled to a bosonic field, Rev. Math. Phys. 10, no.7, 989-1026 (1998)
14. A. Boutet de Monvel-Berthier, V. Georgescu, and A. Soffer, N-body Hamiltonian with hard-core interactions, Rev. Math. Phys. 6, no. 4, 515-596 (1994)
15. J. Walcher, Anwendung positiver Kommutatoren auf den Quanten-Hall-Effekt, ETH-diploma thesis (1998).
16. J. Fröhlich, G.M. Graf, J. Walcher, On the extended nature of edge states of quantum Hall Hamiltonians, math-ph/9903014
17. E. Akkermans, J. E. Avron, R. Narevich, R. Seiler, Boundary conditions for bulk and edge states in quantum Hall systems, SFB 288 Preprint No. 248, TU Berlin 1997, mp-arc 96-646
18. J. E. Avron, R. Seiler, B. Simon, Charge deficiency, charge transport and comparison of dimensions, Commun. Math. Phys. 159, 399 (1994)
19. N. Macris, P. A. Martin, J. V. Pulé, On edge states in semi-infinite quantum Hall systems, J. Phys. A 32, 1985-1996 (1998), cond-mat 9812367
20. S. De Bièvre and J. V. Pulé, private communication; see also Propagating Edge States for a Magnetic Hamiltonian, Math. Phys. Electr. J. 5 (1999), math-ph/9903034
21. R. Joynt and R. E. Prange, Conditions for the Quantum Hall effect, Phys. Rev. B 29, 3303 (1984)
22. D. Lehmann, A microscopic derivation of the critical magnetic field in a Superconductor, Commun. Math. Phys. 173, 155-174 (1995)
23. M. Reed and B. Simon, Methods of modern mathematical physics, vols 1-4, Academic Press 1972-1979
24. H. Kunz, B. Souillard, Sur le spectre des opérateurs aux différences finies aléatoires, Commun. Math. Phys. 78, 201-246 (1980)
25. J. L. Lions and E. Magènes, Non-homogeneous boundary value problems and applications, vol. 1, Springer 1972
26. R.A. Adams, Sobolev spaces, Academic Press (1975).
27. V.I. Burenkov, Sobolev spaces on domains, Teubner (1998).
28. F. G. Tricomi, Fonctions hypergéometriques confluentes, Mémorial des sciences mathématiques CXL (1960)
29. A. Erdélyi et al., Higher Transcendental Functions, vols. I and II, McGraw-Hill 1953