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Lowest energy states in nonrelativistic QED: atoms and ions in motion

Michael Loss·Tadahiro Miyao·Herbert Spohn
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Abstract

Within the framework of nonrelativisitic quantum electrodynamics we consider a single nucleus and $N$ electrons coupled to the radiation field. Since the total momentum $P$ is conserved, the Hamiltonian $H$ admits a fiber decomposition with respect to $P$ with fiber Hamiltonian $H(P)$. A stable atom, resp. ion, means that the fiber Hamiltonian $H(P)$ has an eigenvalue at the bottom of its spectrum. We establish the existence of a ground state for $H(P)$ under (i) an explicit bound on $P$, (ii) a binding condition, and (iii) an energy inequality. The binding condition is proven to hold for a heavy nucleus and the energy inequality for spinless electrons.

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Michael Loss, Tadahiro Miyao, Herbert Spohn. 2006-05-02. Lowest energy states in nonrelativistic QED: atoms and ions in motion. https://arxiv.org/abs/math-ph/0605005

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