Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions

Konstantin Pankrashkin (U Oldenburg)

Nov 11. 2022, 11:00 — 11:30

We consider three-dimensional Dirac operators with arbitrary critical combinations of electrostatic and Lorentz scalar shell interactions supported by a compact smooth surface. It is known from many previous works that the operator shows a loss of regularity in its domain, but the influence of this effect on the spectral properties was not completely clear. We partially close this gap by computing the essential spectrum. It turns out that critical shell interactions lead to the appearance of a whole new interval in the essential spectrum, while the position and the length of the interval are explicitly controlled by the coupling constants and the geometric properties of the shell. This effect is completely new compared to lower dimensional critical situations (in which only a single new point in the essential spectrum appears). Based on joint work with Badreddine Benhellal (Oldenburg).

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory of Differential Operators in Quantum Theory (Workshop)
Jussi Behrndt (TU Graz)
Fritz Gesztesy (Baylor U, Waco)
Ari Laptev (Imperial College London)
Christiane Tretter (U Bern)