Prof. Dirk Hundertmark (Karlsruhe Institut für Technologie) war zu Gast im IADM und sprach am Freitag, den 03. Februar 2023 im Institutskolloquium zum Thema "Quantum systems at the Brink. Subexponential decay bounds for ground states at the edge of the essential spectrum".
Abstract:
Imagine a quantum system where a parameter is tuned in such a way that the ground state energy touches the bottom of the essential spectrum.
Does the ground state survive at critical coupling, or does it disappear?
A well-known example of such a system are helium type atoms at critical coupling, which are an intensely studied problem in quantum chemistry.
We prove sharp non isotropic subexponential bounds for the decay of the ground state for such helium type atoms.
For one-particle Schrödinger operators we also derive complementary necessary and sufficient conditions for the existence, respectively, non-existence of zero energy ground states. Our conditions give a straightforward explanation for the folklore that for these systems, there is a spectral phase transition with critical dimension 4.