Spectral properties of magnetic Hamiltonians (survey)

Hamiltonians in Magnetic Fields

04 September 14:00 - 15:00

Dimitri Yafaev - Université de Rennes 1; St Petersburg State University

We discuss spectral properties of quantum magnetic Hamiltonians for several physically important classes of magnetic fields $B(x,y,z)$: 1. $B(x,y,z)=constant$ 2. $B(x,y,z)$ is a function decaying sufficiently rapidly at infinity In the following two cases $B(x,y,z)$ is translationally invariant, that is, it does not depend on $z$ and $B(x,y)$ decays sufficiently rapidly as $(x,y)\to \infty$ 3. The vectors $B(x,y)$ are directed along the $z$-axis 4. The vectors $B(x,y)$ are orthogonal to the $z$-axis A behavior of the corresponding classical systems is also discussed.
Rafael D. Benguria
Pontificia Universidad Católica de Chile
Arne Jensen
Aalborg University
Georgi Raikov
Pontificia Universidad Católica de Chile
Grigori Rozenblioum
Chalmers/University of Gothenburg
Jan Philip Solovej
University of Copenhagen