## 解析学火曜セミナー

開催情報 火曜日　16:50～18:20　数理科学研究科棟(駒場) 128号室 石毛 和弘, 坂井 秀隆, 伊藤 健一 https://www.ms.u-tokyo.ac.jp/seminar/analysis/

### 2013年07月09日(火)

16:30-18:00   数理科学研究科棟(駒場) 118号室
Tom\'as Lungenstrass 氏 (Pontificia Universidad Catolica de Chile)
A Trace Formula for Long-Range Perturbations of the Landau Hamiltonian
(Joint work with Georgi Raikov) (ENGLISH)
[ 講演概要 ]
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.