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arXiv · 2010.08452

The absence of the Efimov effect in systems of one- and two-dimensional particles

Simon Barth·Andreas Bitter·Semjon Vugalter
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Abstract

We study virtual levels of $N$-particle Schr\"odinger operators and prove that if the particles are one-dimensional and $N\ge 3$, then virtual levels at the bottom of the essential spectrum correspond to eigenvalues. The same is true for two-dimensional particles if $N\ge 4$. These results are applied to prove the non-existence of the Efimov effect in systems of $N\ge 4$ one-dimensional or $N\ge 5$ two-dimensional particles.

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Simon Barth, Andreas Bitter, Semjon Vugalter. 2020-10-16. The absence of the Efimov effect in systems of one- and two-dimensional particles. https://doi.org/10.1063/5.0033524

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