Classical and Quantum Integrability

2-6 September 2019
Institut de Mathématiques de Bourgogne
Europe/Paris timezone

A hybrid WKB-based method for Schrödinger scattering problems in the semi-classical limit

3 Sep 2019, 11:45
45m
Amphi Gevrey ()

Speaker

Anton Arnold (Vienna University of Technology)

Description

We consider 1D scattering problems related to quantum transport in diodes. We discuss the efficient numerical integration of ODEs like $\epsilon^2*u"+a(x)*u=0$ for $0<\epsilon<<1$ on coarse grids, but still yielding accurate solutions; including oscillatory (for given $a(x)>0$) and evanescent regimes (for $a(x)<0$), partly including turning points. In the oscillatory case we use a marching method that is based on an analytic WKB-preprocessing of the equation. And in the evanescent case we use a FEM with WKB-ansatz functions.

(co-authors: Claudia Negulescu; Kirian Döpfner; Christian Klein, Bernhard Ujvari)

Primary author

Anton Arnold (Vienna University of Technology)