Tuesday Seminar of Analysis
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Date, time & place | Tuesday 16:00 - 17:30 156Room #156 (Graduate School of Math. Sci. Bldg.) |
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Organizer(s) | ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi |
2013/07/09
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Tom\'as Lungenstrass (Pontificia Universidad Catolica de Chile)
A Trace Formula for Long-Range Perturbations of the Landau Hamiltonian
(Joint work with Georgi Raikov) (ENGLISH)
Tom\'as Lungenstrass (Pontificia Universidad Catolica de Chile)
A Trace Formula for Long-Range Perturbations of the Landau Hamiltonian
(Joint work with Georgi Raikov) (ENGLISH)
[ Abstract ]
The Landau Hamiltonian describes the dynamics of a two-dimensional
charged particle subject to a constant magnetic field. Its spectrum
consists in eigenvalues of infinite multiplicity given by $B(2q+1)$, $q\\in Z_+$. We
consider perturbations of this operator by including a continuous
electric potential that decays slowly at infinity (as $|x|^{-\\rho}$, $0<\\rho<1$).
The spectrum of the perturbed operator consists of eigenvalue clusters
which accumulate to the Landau levels. We provide estimates for the
rate at which the clusters shrink as we move up the energy levels.
Further, we obtain an explicit description of the asymptotic density
of eigenvalues for asymptotically homogeneous long-range potentials in
terms of a mean-value transform of the associated homogeneous
function.
The Landau Hamiltonian describes the dynamics of a two-dimensional
charged particle subject to a constant magnetic field. Its spectrum
consists in eigenvalues of infinite multiplicity given by $B(2q+1)$, $q\\in Z_+$. We
consider perturbations of this operator by including a continuous
electric potential that decays slowly at infinity (as $|x|^{-\\rho}$, $0<\\rho<1$).
The spectrum of the perturbed operator consists of eigenvalue clusters
which accumulate to the Landau levels. We provide estimates for the
rate at which the clusters shrink as we move up the energy levels.
Further, we obtain an explicit description of the asymptotic density
of eigenvalues for asymptotically homogeneous long-range potentials in
terms of a mean-value transform of the associated homogeneous
function.