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Counting negative eigenvalues with index theory
15 Dec
15. December 2023
Oberseminar Analysis

Counting negative eigenvalues with index theory

In this talk we will consider the Pauli Hamiltonian, a Schrödinger operator describing a spin particle moving in a magnetic field in two dimensions. The problem we will discuss is that of describing how many negative eigenvalues there are for its Neumann realization on a compact domain. We provide a sharp lower bound for the number of negative eigenvalues by means of a connection to Atiyah-Patodi-Singer’s index theorem for Dirac operators arising from an elementary integration by parts. We conclude an asymptotic formula for the counting function of the semiclassical Landau-Neumann Hamiltonian below the first Landau level as hbar goes to zero.

Joint work with Søren Fournais, Rupert Frank, Ayman Kachmar and Mikael Persson-Sundqvist.

Speaker

Prof. Dr. Magnus Goffeng
Lund University

Organiser

Institut für Analysis

Date

15. December 2023
14:00 o'clock - 16:00 o'clock

Public contact

Institut für Analysis

Location

Hauptgebäude
Building: 1101
Room: g123
Welfengarten 1
30167 Hannover
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