Discrete spectrum of quantum Hall effect Hamiltonians I. Monotone edge potentials

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dc.contributor.authorBruneau, Vincent
dc.contributor.authorMiranda, Pablo
dc.contributor.authorRaikov, Georgi
dc.date.accessioned2024-01-10T12:04:58Z
dc.date.available2024-01-10T12:04:58Z
dc.date.issued2011
dc.description.abstractWe 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.format.extent36 páginas
dc.fuente.origenWOS
dc.identifier.doi10.4171/JST/11
dc.identifier.eissn1664-0403
dc.identifier.issn1664-039X
dc.identifier.urihttps://doi.org/10.4171/JST/11
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/75918
dc.identifier.wosidWOS:000209021500001
dc.information.autorucMatemática;Georgi D. Raikov;S/I;1004967
dc.issue.numero3
dc.language.isoen
dc.nota.accesoSin adjunto
dc.pagina.final272
dc.pagina.inicio237
dc.publisherEUROPEAN MATHEMATICAL SOC
dc.revistaJOURNAL OF SPECTRAL THEORY
dc.rightsregistro bibliográfico
dc.subjectMagnetic Schrodinger operators
dc.subjectspectral gaps
dc.subjecteigenvalue distribution
dc.subject.ods04 Quality Education
dc.subject.odspa04 Educación y calidad
dc.titleDiscrete spectrum of quantum Hall effect Hamiltonians I. Monotone edge potentials
dc.typeartículo
dc.volumen1
sipa.codpersvinculados1004967
sipa.indexWOS
sipa.trazabilidadCarga SIPA;09-01-2024
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