Discrete spectrum of quantum Hall effect Hamiltonians II: Periodic edge potentials

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dc.contributor.authorMiranda, Pablo
dc.contributor.authorRaikov, Georgi
dc.date.accessioned2024-01-10T12:04:57Z
dc.date.available2024-01-10T12:04:57Z
dc.date.issued2012
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 = (W) over bar is a T-periodic 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 sigma(H-0) of H-0 has a band structure, the band functions are bT-periodic, and generically there are infinitely many open gaps in sigma(H-0). We establish explicit sufficient conditions which guarantee that a given band of sigma(H-0) has a positive length, and all the extremal points of the corresponding band function are non-degenerate. Under these assumptions 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 could be interpreted as a 1D Schrodinger operator with infinite-matrix-valued potential. Further, we restrict our attention on perturbations V of compact support. We find that there are infinitely many discrete eigenvalues in any open gap in the spectrum sigma(H-0), and the convergence of these eigenvalues to the corresponding spectral edge is asymptotically Gaussian.
dc.description.funderChilean Science Foundation Fondecyt
dc.description.funderNucleo Cientifico ICM
dc.fechaingreso.objetodigital2024-05-23
dc.format.extent21 páginas
dc.fuente.origenWOS
dc.identifier.doi10.3233/ASY-2012-1103
dc.identifier.issn0921-7134
dc.identifier.urihttps://doi.org/10.3233/ASY-2012-1103
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/75917
dc.identifier.wosidWOS:000309213900006
dc.information.autorucMatemática;Raikov G;S/I;1004967
dc.issue.numero3-4
dc.language.isoen
dc.nota.accesocontenido parcial
dc.pagina.final345
dc.pagina.inicio325
dc.publisherIOS PRESS
dc.revistaASYMPTOTIC ANALYSIS
dc.rightsacceso restringido
dc.subjectmagnetic Schrodinger operators
dc.subjectspectral gaps
dc.subjecteigenvalue distribution
dc.subjectRANDOM LANDAU HAMILTONIANS
dc.subjectCONSTANT MAGNETIC-FIELDS
dc.subjectSCHRODINGER-OPERATORS
dc.subjectASYMPTOTICS
dc.subject.ods04 Quality Education
dc.subject.odspa04 Educación y calidad
dc.titleDiscrete spectrum of quantum Hall effect Hamiltonians II: Periodic edge potentials
dc.typeartículo
dc.volumen79
sipa.codpersvinculados1004967
sipa.indexWOS
sipa.trazabilidadCarga SIPA;09-01-2024
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