Aarhus Universitets segl

Pseudodifferential expression for the S-matrix of a perturbed Stark Hamiltonian

Kenichi Ito (Graduate School of Mathematical Sciences, University of Tokyo)
Mathematics seminar
Onsdag, 28. september, 2022 | 16:00–17:00 | Aud. D3 (1531-215)
Kontakt: Erik Skibsted

We discuss the one-body Stark Hamiltonian with a short-range perturbation. We formulate the S-matrix by the asymptotics of generalized eigenfunctions, and prove that it is a pseudodifferential operator. We can compute its leading symbol in terms of the perturbation. The proof depends on microlocal analysis endowed with the Fourier-Airy phase as well as on Sommerfeld's uniqueness result. Our approach can be viewed as an adaption of the method of Isozaki-Kitada for the Schr\"odinger operators with decaying potentials. It is more flexible and informative than the method by Kvitsinsky-Kostrykin. This talk is based on a joint work with Erik Skibsted.