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arXiv · 1805.00191

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

Dinh-Thi Nguyen
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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.

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Dinh-Thi Nguyen. 2018-05-01. Many-Body Blow-Up Profile of Boson Stars with External Potentials. https://doi.org/10.1142/s0129055x1950034x

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