Multiscale Theory of Finite Size Bose Systems: Implications for Collective and Single-Particle Excitations

TL;DR

This paper develops a multiscale theoretical framework to analyze finite size Bose systems, revealing how collective and single-particle behaviors manifest and vary with interatomic forces, with applications to Helium-4 nanodroplets.

Contribution

It introduces a multiscale wave equation approach for finite Bose systems, providing insights into the interplay of collective and single-particle excitations and surpassing traditional field theoretic methods.

Findings

Short-range wave function structure diminishes as interatomic forces weaken.

Residual short-range structure increases with stronger interatomic forces.

Methodology applies broadly to finite Bose systems, including Helium-4 nanodroplets.

Abstract

Boson droplets (i.e., dense assemblies of bosons at low temperature) are shown to mask a significant amount of single-particle behavior and to manifest collective, droplet-wide excitations. To investigate the balance between single-particle and collective behavior, solutions to the wave equation for a finite size Bose system are constructed in the limit where the ratio \varepsilon of the average nearest-neighbor boson distance to the size of the droplet or the wavelength of density disturbances is small. In this limit, the lowest order wave function varies smoothly across the system, i.e., is devoid of structure on the scale of the average nearest-neighbor distance. The amplitude of short range structure in the wave function is shown to vanish as a power of \varepsilon when the interatomic forces are relatively weak. However, there is residual short range structure that increases with the strength of interatomic forces. While the multiscale approach is applied to boson droplets, the methodology is applicable to any finite size bose system and is shown to be more direct than field theoretic methods. Conclusions for Helium-4 nanodroplets are drawn.