Related papers: Rigorous derivation of the Efimov effect in a simple model

Rigorous derivation of the Efimov effect in a simple model

URL: http://arxiv.org/abs/2306.12157v1
Date: Wed, 21 Jun 2023 10:11:28 GMT
Title: Rigorous derivation of the Efimov effect in a simple model
Authors: Davide Fermi, Daniele Ferretti, Alessandro Teta
Abstract summary: We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
Score: 68.8204255655161
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We consider a system of three identical bosons in $\mathbb{R}^3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$. Using a quadratic form approach we prove that the corresponding Hamiltonian is self-adjoint and bounded from below for any value of $a$. In particular this means that the hard-core repulsion is sufficient to prevent the fall to the center phenomenon found by Minlos and Faddeev in their seminal work on the three-body problem in 1961. Furthermore, in the case of infinite two-body scattering length, also known as unitary limit, we prove the Efimov effect, \emph{i.e.}, we show that the Hamiltonian has an infinite sequence of negative eigenvalues $E_n$ accumulating at zero and fulfilling the asymptotic geometrical law $\;E_{n+1} / E_n \; \to \; e^{-\frac{2\pi}{s_0}}\,\; \,\text{for} \,\; n\to +\infty$ holds, where $s_0\approx 1.00624$.

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