Discrete spectrum of quantum Hall effect Hamiltonians I. Monotone edge potentials
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BRUNEAU, Vincent | |
| hal.structure.identifier | Facultad de Matemáticas [Santiago de Chile] | |
| dc.contributor.author | RAIKOV, Georgi | |
| hal.structure.identifier | Facultad de Matemáticas [Santiago de Chile] | |
| dc.contributor.author | MIRANDA, Pablo | |
| dc.date.accessioned | 2024-04-04T02:18:17Z | |
| dc.date.available | 2024-04-04T02:18:17Z | |
| dc.date.issued | 2011 | |
| dc.identifier.issn | 1664-039X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189298 | |
| dc.description.abstractEn | We consider the unperturbed operator H-0 = (-i del - A)(2) + W, self-adjoint in L-2(R-2). Here A is a magnetic potential which generates a constant magnetic field b > 0, and the edge potential W is a non-decreasing non-constant bounded function depending only on the first coordinate x is an element of R of (x, y) is an element of R-2. Then the spectrum of H-0 has a band structure and is absolutely continuous; moreover, the assumption lim(x ->infinity)(W(x) - W(-x)) < 2b implies the existence of infinitely many spectral gaps for H-0. We consider the perturbed operators H-+/- = H-0 +/- V where the electric potential V is an element of L-infinity(R-2) is non-negative and decays at infinity. We investigate the asymptotic distribution of the discrete spectrum of H-+/- in the spectral gaps of H-0. We introduce an effective Hamiltonian which governs the main asymptotic term; this Hamiltonian involves a pseudo-differential operator with generalized anti-Wick symbol equal to V. Further, we restrict our attention on perturbations V of compact support and constant sign. We establish a geometric condition on the support of V which guarantees the finiteness of the number of the eigenvalues of H-+/- in any spectral gap of H-0. In the case where this condition is violated, we show that, generically, the convergence of the infinite series of eigenvalues of H+ (resp. H-) to the lower (resp. upper) edge of a given spectral gap, is Gaussian. | |
| dc.language.iso | en | |
| dc.publisher | European Mathematical Society | |
| dc.title.en | Discrete spectrum of quantum Hall effect Hamiltonians I. Monotone edge potentials | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.4171/JST/11 | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| bordeaux.journal | Journal of Spectral Theory | |
| bordeaux.page | 237-272 | |
| bordeaux.volume | 1 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00988977 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00988977v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Spectral%20Theory&rft.date=2011&rft.volume=1&rft.issue=3&rft.spage=237-272&rft.epage=237-272&rft.eissn=1664-039X&rft.issn=1664-039X&rft.au=BRUNEAU,%20Vincent&RAIKOV,%20Georgi&MIRANDA,%20Pablo&rft.genre=article |
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