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arXiv:2602.05942

On the Efimov Effect for Four Particles in Dimension Two

Jonathan Rau, Marvin R. Schulz

math-phquant-phSubmitted Feb 5, 2026• Announced Feb 6, 2026• 0 citations
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Abstract

We prove that the Schrödinger operator describing four particles in two dimensions, interacting solely through short-range three-body forces, can possess infinitely many bound states. This holds under the assumption that each three-body subsystem has a virtual level at zero energy. Our result establishes an analog of the Efimov effect for such four-particle systems in two dimensions.

Comments
58 pages and three figures

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We prove that the Schrödinger operator describing four particles in two dimensions, interacting solely through short-range three-body forces, can possess infinitely many bound states. This holds under the assumption that each three-body subsystem has a virtual level at zero energy. Our result establishes an analog of the Efimov effect for such four-particle systems in two dimensions.
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