Spectral properties of Landau Hamiltonians with non-local potentials

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dc.contributor.authorCardenas, Esteban
dc.contributor.authorRaikov, Georgi
dc.contributor.authorTejeda, Ignacio
dc.date.accessioned2025-01-23T19:47:17Z
dc.date.available2025-01-23T19:47:17Z
dc.date.issued2020
dc.description.abstractWe consider the Landau Hamiltonian H-0, self-adjoint in L-2 (R-2), whose spectrum consists of an arithmetic progression of infinitely degenerate positive eigenvalues Lambda(q), q is an element of Z(+). We perturb H-0 by a non-local potential written as a bounded pseudo-differential operator Op(w)(V) with real-valued Weyl symbol V, such that Op(w)(V)H-0(-1) is compact. We study the spectral properties of the perturbed operator H-V = H-0 Op(w)(V). First, we construct symbols V, possessing a suitable symmetry, such that the operator H-V admits an explicit eigenbasis in L-2 (R-2), and calculate the corresponding eigenvalues. Moreover, for V which are not supposed to have this symmetry, we study the asymptotic distribution of the eigenvalues of H-V adjoining any given Lambda(q). We find that the effective Hamiltonian in this context is the Toeplitz operator T-q(V) = p(q)Op(w)(V)p(q), where p(q) is the orthogonal projection onto Ker(H-0 - Lambda I-q), and investigate its spectral asymptotics.
dc.description.funderChilean Science Foundation Fondecyt
dc.fuente.origenWOS
dc.identifier.doi10.3233/ASY-191591
dc.identifier.eissn1875-8576
dc.identifier.issn0921-7134
dc.identifier.urihttps://doi.org/10.3233/ASY-191591
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/100368
dc.identifier.wosidWOS:000587721500006
dc.issue.numero3-4
dc.language.isoen
dc.pagina.final371
dc.pagina.inicio337
dc.revistaAsymptotic analysis
dc.rightsacceso restringido
dc.subjectLandau Hamiltonian
dc.subjectnon-local potentials
dc.subjectWeyl pseudo-differential operators
dc.subjecteigenvalue asymptotics
dc.subjectlogarithmic capacity
dc.titleSpectral properties of Landau Hamiltonians with non-local potentials
dc.typeartículo
dc.volumen120
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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