The No-Binding Regime of the Pauli-Fierz Model

Details The No-Binding Regime of the Pauli-Fierz Model The No-Binding Regime of the Pauli-Fierz Model

2011-04-06

arxiv.org/abs/1104.0990v1

Physics

Mathematical Physics

18 pages and 1 figure

Scientific paper

The Pauli-Fierz model $H(\alpha)$ in nonrelativistic quantum electrodynamics is considered. The external potential $V$ is sufficiently shallow and the dipole approximation is assumed. It is proven that there exist constants $0<\alpha_-< \alpha_+$ such that $H(\alpha)$ has no ground state for $|\alpha|<\alpha_-$, which complements an earlier result stating that there is a ground state for $|\alpha| > \alpha_+$. We develop a suitable extension of the Birman-Schwinger argument. Moreover for any given $\delta>0$ examples of potentials $V$ are provided such that $\alpha_+-\alpha_-<\delta$.

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