Effective Dynamics of Translationally Invariant Magnetic Schrödinger Equations in the High Field Limit
arxiv(2022)
摘要
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∈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.
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