Evelyn Richman | Searcharxiv

arXiv2024

Effective Dynamics of Translationally Invariant Magnetic Schrödinger Equations in the High Field Limit

We study the large field limit in Schrödinger equations with magnetic vector potentials describing translationally invariant $B$-fields with respect to the $z$-axis. In a first step, using regular perturbation theory, we derive an approximate description of the solution, provided the initial data is compactly supported in the Fourier-variable dual to $z\in \mathbb R$. The effective dynamics is thereby seen to produce high-frequency oscillations and large magnetic drifts. In a second step we show, by using the theory of almost invariant subspaces, that this asymptotic description is stable under polynomially bounded perturbations that vanish in the vicinity of the origin.

math-ph↗

arXiv2021

Strong Magnetic Field Limit in a Nonlinear Iwatsuka-Type Model

We study the strong magnetic field limit for a nonlinear Iwatsuka-type model, i.e. a nonlinear Schrödinger equation in two spatial dimensions with a magnetic vector potential that only depends on the $x$-coordinate. Using a high-frequency averaging technique, we show that this equation can be effectively described by a nonlocal nonlinear model, which is no longer dispersive. We also prove that, in this asymptotic regime, inhomogeneous nonlinearities are confined along the $y$-axis.

math.AP↗