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

Abstract

We study virtual levels of $N$-particle Schrödinger 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.

51 pages

References in corpus (4)

• Evidence for Universal Four-Body States Tied to an Efimov Trimer
• Study of Efimov physics in two nuclear-spin sublevels of 7Li
• Proof of the Super Efimov Effect
• Why there is no Efimov effect for four bosons and related results on the finiteness of the discrete spectrum

Cited by in corpus (2)

• Quantum Systems at the Brink: Existence of Bound States, Critical Potentials and Dimensionality
• Semisuper Efimov effect induced by resonant pair exchange in mixed dimensions