News und Vorträge
News
Vorträge der nächsten sieben Tage
Benjamin Brotz:
Relativistic $\delta$-shell interactions
Montag, 28.7.25, 16:15-17:45, Seminarraum 404
Abstract: In quantum mechanics, the practice of coupling Hamiltonians with singular potentials supported on lower-dimensional subsets of the ambient space is a well-established concept. For instance, the physicists Ralph Kronig and William Penney had already considered Schrödinger operators coupled with $\delta$-point potentials in their 1931 work, "Quantum mechanics of electrons in crystal lattices.“
However, one should remember that such $\delta$-potentials are merely idealized representations of real-world physical phenomena. Therefore, understanding how these operators can be rigorously approximated by more regular potentials is important for their physical interpretation and mathematical validity.
In this talk, we will present a result by Albert Mas and Fabio Pizzichillo which shows that the Dirac operator on $\mathbb{R}^{3}$ coupled with suitable short-range potentials converges in the strong resolvent sense to the Dirac operator coupled with a $\delta$-potential supported on the boundary of a $C^{2}$ domain. Following this, we'll discuss a possible generalization of this result to more general spinor bundles.
Kang Zuo: (Universität Mainz)
Loci of non-rigid families of varieties in corresponding moduli spaces
Dienstag, 29.7.25, 16:00-17:30, Seminarraum 125