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/s
Prof. Dr. Magnus Goffeng
Lund University
Event organiser/s
Institut für Analysis
Date
15. December 202314:00 o'clock - 16:00 o'clock
Contact information
Institut für AnalysisLocation
HauptgebäudeBuilding: 1101
Room: g123
Welfengarten 1
30167 Hannover