Zero modes in a system of Aharonov-Bohm solenoids on the Lobachevsky plane

Journal of Physics A: Mathematical and General

Volumn 39, Issue 6, 2006, Pages 1375-1384

  Geyler, V A ^a   StOvicek P ^b  

^a OGAREV MORDOVIA STATE UNIVERSITY   (Russian Federation)

^b CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31344473452     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/39/6/011     Document Type: Article

References (24)

1. Aharonov Y and Casher A 1979 Ground state of a spin 1/2 charged particle in a two-dimensional magnetic field Phys. Rev. A 19 2461-2
2. Albeverio S, Exner P and Geyler V A 2001 Geometric phase related to point-interaction transport on a magnetic lobachevsky plane Lett. Math. Phys. 55 9-16
3. Arai A 1993 Properties of the Dirac-Weyl operator with a strongly singular gauge potential J. Math. Phys. 34 915-35
4. Bellissard J, van Elst A and Schulz-Baldes H 1994 The noncommutative geometry of the quantum Hall effect J. Math. Phys. 35 5373-451
5. Brouwer P W, Racine E, Furusaki A, Hatsugai Y, Morita Y and Mudry C 2002 Zero-modes in the random Hopping model Phys. Rev. B 66 014204
6. Carey A L, Hannabus K C, Mathai V and McCann P 1998 Quantum Hall effect on the hyperbolic plane Commun. Math. Phys. 190 629-73
7. Carey A L, Hannabus K C and Mathai V 1999 Quantum Hall effect on the hyperbolic plane in the presence of disorder Lett. Math. Phys. 47 215-36
8. Comtet A 1987 On the Landau levels on the hyperbolic plane Ann. Phys. 173 185-209
9. Desbois J, Furtlehner C and Ouvry S 1995 Random magnetic impurities and the Landau problem Nucl. Phys. B 453 [FS] 759-76
10. Ferapontov E V and Veselov A P 2001 Integrable schrödinger operators with magnetic fields: factorization method on curved surfaces J. Math. Phys. 42 590-607
11. Ford L R 1951 Automorphic functions (New York: Chelsea)
12. Geyler V A and Grishanov E N 2002 Zero modes in a periodic system of Aharonov-Bohm solenoids Pis'ma Zh. Eksper. Teor. Fiz. 75 425-7 (in Russian)
13. Geyler V A and Grishanov E N 2002 JETP Lett. 75 354-6 (Engl. Transl.)
14. Geyler V A and Šťovíček P 2004 Zero modes in a system of Aharonov-Bohm fluxes Rev. Math. Phys. 16 851-907
15. Kohmoto M 1989 Zero modes and the quantized Hall conductance of the two dimensional lattice in a magnetic field Phys. Rev. B 39 11943-9
16. Kra I 1972 Automorphic forms and Kleinian groups (Reading, MA: Benjamin)
17. Marcolli M and Mathai V 2006 Towards the fractional quantum Hall effect: a noncommutative geometry perspective Noncommutative Geometry, Arithmetic, and Physics ed C Consani and M Marcolli (Wiesbaden: Vieweg Verlag) (Preprint cond-mat/0502356) to appear
18. Prinz V Ya, Seleznev V A, Samoylov V A and Gutakovsky A K 1996 Nanoscale engineering using controllable formation of ultra-thin cracks in heterostructures Microelectron. Eng. 30 439-42
19. Rozenblum G V and Shirokov N 2005 Infiniteness of zero modes for the Pauli operator with singular magnetic field Preprint math-ph/0501059
20. Scuseria G E 1992 Negative curvature and hyperfullerenes Chem. Phys. Lett. 195 534-6
21. Sitenko Yu A 1989 Zero-modes of the Dirac operator on a noncompact two-dimensional surface in a magnetic field Yad. Fiz. 50 901-6 (in Russian)
22. Sitenko Yu A 1989 Soviet J. Nucl. Phys. 50 561-4 (Engl. Transl.)
23. Terrones H and Terrones M 2003 Curved nanostructured materials New J. Phys. 5 126
24. Thienel M 2000 Quantum mechanics of an electron in a homogeneous magnetic field and a singular magnetic flux tube Ann. Phys. 280 140-62