Seminar

Absence of positive eigenvalues for hard-core $N$-body systems

Hamiltonians in Magnetic Fields

25 October 14:00 - 15:00

Erik Skibsted - Aarhus University

We give an account of a recent joint work with K. Ito on absence of positive eigenvalues for generalized $2$-body hard-core Schrödinger operators. We show absence of such eigenvalues under the condition of bounded strictly convex obstacles. A scheme for showing absence of positive eigenvalues for generalized $N$-body hard-core Schrödinger operators, $N\geq 2$, is presented. This scheme involves high energy resolvent estimates, and for $N=2$ it is implemented by a Mourre commutator type method. A particular example is the Helium atom with the assumption of infinite mass and finite extent nucleus.
Organizers
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