On the essential spectrum of two-dimensional periodic magnetic Schrödinger operators

Letters in Mathematical Physics

Volumn 49, Issue 3, 1999, Pages 197-211

  Cornean, H D ^a  

^a INSTITUTE OF MATHEMATICS   (Romania)

Author keywords

Essential spectrum; Magnetic field; Schr dinger operators

Indexed keywords

EID: 0010569122     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007623907088     Document Type: Article

References (17)

1. Briet, P., Combes, J. M. and Duclos, P.: Spectral stability under tunneling, Comm. Math. Phys. 126 (1989), 133.
2. Cycon, H. L., Froese, R. G., Kirsch, W. and Simon, B.: Schrödinger Operators with Application to Quantum Mechanics and Global Geometry, Springer-Verlag, Berlin, 1987.
3. Cornean, H. D. and Nenciu, G.: On eigenfunction decay of two dimensional magnetic Schrödinger operators, Comm. Math. Phys. 192 (1998), 671.
4. Cornean, H. D. and Nenciu, G.: Two dimensional magnetic Schrödinger operators: width of mini-bands in the tight binding approximation, Preprint E.S.I. 608, Vienna, 1998. To appear in Ann. Inst. H. Poincaré Phys. Théor.
5. Daumer, F.: Equation de Schrödinger avec champ éléctrique périodique et champ magnétique constant dans l'approximation du tight-binding, Comm. Partial Differential Equations 18 (5, 6) (1993), 1021.
6. Helffer, B.: On spectral theory for Schrödinger operators with magnetic potentials, Adv. Stud Pure Math. 23 (1994), 113.
7. Hempel, R. and Herbst I.: Strong magnetic fieds, Dirichlet boundaries and spectral gaps, Preprint E.S.I. 74, Vienna, 1994.
8. Helffer, B. and Sjöstrand, J.: Multiple wells in the semi-classical limit I, Comm. Partial Differential Equations 9 (1984), 337.
9. Helffer, B. and Sjöstrand, J.: Puits multiples en limite semi-classique II, Interaction moléculaire. Symétries. Perturbations, Ann. Inst. H. Poincaré 42 (1985), 127.
10. Helffer, B. and Sjöstrand, J.: Multiple wells in the semi-classical limit III, Math. Nachr. 124 (1985), 263.
11. Helffer, B. and Sjöstrand, J.: Effet tunnel pour l'équation de Schrödinger avec champ magnétique, Ann. École Pise. 14 (1987), 625.
12. Helffer, B. and Sjöstrand, J.: Equation de Schrödinger avec champ magnétique et équation de Harper, In: Lecture Notes in Phys. 34, Springer-Verlag, New York, 1988, pp. 118-197.
13. Iwatsuka, A.: The essential spectrum of two dimensional Schrödinger operators with perturbed magnetic fields, J. Math. Kyoto Univ. 23 (1983), 475.
14. Nakamura, S.: Band Spectrum for Schrödinger Operators with Strong Periodic Magnetic Fields, Oper. Theory: Adv. Appl. 78, Birkhäuser, Basel, 1995.
15. Nenciu, G.: Dynamics of band electrons in electric and magnetic fields: rigorous justification of the effective Hamiltonians. Rev. Mod. Phys. 63 (1991), 91.
16. Simon, B.: Schrödinger semigroups. Bull. Amer. Math. Soc: (N.S.) 7 (1982), 447.
17. Thaller, B.: The Dirac Equation, Springer-Verlag, Berlin, 1992.