Many-Body Blow-Up Profile of Boson Stars with External Potentials

TL;DR

This paper analyzes the blow-up behavior of ground states in a large bosonic quantum system under attractive interactions and external trapping, revealing that the blow-up profile aligns with Gagliardo-Nirenberg solutions.

Contribution

It provides a detailed description of the blow-up profile of boson star ground states near the critical interaction strength as the number of particles grows.

Findings

Ground state energy blows up as interaction approaches critical value.

Blow-up profile matches Gagliardo-Nirenberg solutions.

Results extend understanding of boson star stability and collapse.

Abstract

We consider a 3D quantum system of $N$ identical bosons in a trapping potential $|x|^p$, with $p\geq0$, interacting via a Newton potential with an attractive interaction strength $a_{N}$. For a fixed large $N$ and the coupling constant $a_{N}$ smaller than a critical value $a_{*}$ (Chandrasekhar limit mass), in an appropriate sense, the many-body system admits a ground state. We investigate the blow-up behavior of the ground state energy as well as the ground states when $a_{N}$ approaches $a_{*}$ sufficiently slowly in the limit $N\to\infty$. The blow-up profile is given by the Gagliardo-Nirenberg solutions.