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

Abstract

We consider a 3D quantum system of $N$ identical bosons in a trapping potential $|x{|}^p$, with $p\ge 0$, 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 $a_{\ast }$ (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 $a_{\ast }$ sufficiently slowly in the limit $N\to \infty$. The blow-up profile is given by the Gagliardo-Nirenberg solutions.

To appear in Reviews in Mathematical Physics

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Cited by in corpus (3)

• Stabilization against collapse of 2D attractive Bose-Einstein condensates with repulsive, three-body interactions
• Blow-Up Profile of 2D Focusing Mixture Bose Gases
• Blow-up profile of neutron stars in the Hartree-Fock-Bogoliubov theory