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arXiv · 2110.11942

On semi-classical spectral series for an atom in a periodic polarized electric field

Abdelwaheb Ifa·Hanen Louati·Michel Rouleux
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Abstract

In this report we present preliminary results about the tunneling problem for a magnetic Schr\"odinger operator. As a motivation we consider the 3-D time-dependent Schr\"odinger operator $H(t)=-h^2\Delta+V+E(t)\cdot x$ where $V$ is a radial potential and $E(t)$ a circularly polarized field with uniform frequency $\omega$. The quantum monodromy operator (QMO) that takes the system through a complete period $T=2\pi/\omega$, turns out to be unitarily equivalent to $e^{iTP_A(x,hD_x)/h}$, where $P_A(x,hD_x))$ identifies with a magnetic Schr\"odinger operator. When $V$ is sufficiently confining, $P_A(x,hD_x))$ presents a double magnetic well. Then we construct its semi-classical ground state and examine the splitting between its two first eigenvalues.

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Abdelwaheb Ifa, Hanen Louati, Michel Rouleux. 2021-10-22. On semi-classical spectral series for an atom in a periodic polarized electric field. https://arxiv.org/abs/2110.11942

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