Efimov spectrum in bosonic systems with increasing number of particles

TL;DR

This paper investigates the Efimov effect and discrete scaling invariance in systems of up to 16 bosons with large scattering length, extending Efimov's radial law beyond three particles.

Contribution

It extends the analysis of Efimov physics and discrete scaling invariance to N-body bosonic systems, providing universal ratios and generalizing Efimov's radial law.

Findings

Identification of universal energy ratios for N-boson systems

Extension of Efimov radial law to systems with N>3

Evidence of discrete scaling invariance in larger bosonic clusters

Abstract

It is well-known that three-boson systems show the Efimov effect when the two-body scattering length $a$ is large with respect to the range of the two-body interaction. This effect is a manifestation of a discrete scaling invariance (DSI). In this work we study DSI in the $N$-body system by analysing the spectrum of $N$ identical bosons obtained with a pairwise gaussian interaction close to the unitary limit. We consider different universal ratios such as $E_N^0/E_3^0$ and $E_N^1/E_N^0$, with $E_N^i$ being the energy of the ground ($i=0$) and first-excited ($i=1$) state of the system, for $N\le16$. We discuss the extension of the Efimov radial law, derived by Efimov for $N=3$, to general $N$.