Structural and quantum properties of van der Waals cluster near the unitary regime

TL;DR

This paper investigates the universal structural and quantum properties of three-dimensional bosonic van der Waals clusters near the unitary regime, revealing extended states, universal energies, and signs of quantum chaos.

Contribution

It introduces a comprehensive analysis of van der Waals clusters near unitarity, including all two-body correlations and spectral statistics, highlighting universal behaviors and complex quantum dynamics.

Findings

Spatially extended states with exponential level dependence

Universal ground state energy at large negative scattering length

Semi-Poisson spectral statistics indicating quantum complexity

Abstract

We study the structural and several quantum properties of three-dimensional bosonic cluster interacting through van der Waals potential at large scattering length. We use Faddeev-type decomposition of the many-body wave function which includes all possible two-body correlations. At large scattering length, we observe spatially extended states which exhibit the exponential dependence on the state number. The cluster ground state energy shows universal nature at large negative scattering length. We also find the existence of generalized Tjon lines for $N$- body clusters. Signature of universal behaviour of weakly bound clusters can be observed in experiments of ultracold Bose gases. We also study the spectral statistics of the system. We calculate both the short-range fluctuation and long-range.correlation and observe semi-Poisson distribution which interpolates the Gaussian Orthogonal Ensemble (GOE) and Poisson statistics of random matrix theory. It indicates that the van der Waal cluster near the unitary becomes highly complex and correlated. However additional study of $P(r)$ distribution (without unfolding of energy spectrum) reveals the possibility of chaos for larger cluster.