The APDE seminar on Monday, 4/19, will be given by Namaluba Malawo online via Zoom from 4:10 to 5:00pm. To participate, email Georgios Moschidis (gmoschidis@berkeley.edu) or Federico Pasqualotto (fpasqualotto@berkeley.edu).

Title: Resonances for thin barriers on the half-line.

Abstract: The analysis of scattering by thin barriers is important for many physical problems, including quantum corrals. To model such a barrier, we use a delta function potential on the half-line. Our main results compute decay rates for particles confined by this barrier. The decay rates are given by imaginary parts of resonances. We show that they energy dependence of the decay rates is logarithmic when the barrier is weaker and polynomial when the barrier is stronger. To compute them, we derive a formula for resonances in terms of the Lambert W function and apply a series expansion. Joint work with Kiril Datchev.