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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.00784 |
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Table of Contents:
- We consider dilute Bose gases on the three dimensional unit torus that interact through a pair potential with scattering length of order $ N^{κ-1}$, for some $κ>0$. For the range $ κ\in [0, \frac1{43})$, \cite{ABS} proves complete BEC of low energy states into the zero momentum mode based on a unitary renormalization through operator exponentials that are quartic in creation and annihilation operators. In this paper, we give a new and self-contained proof of BEC of the ground state for $ κ\in [0, \frac1{20})$ by combining some of the key ideas of \cite{ABS} with the novel diagonalization approach introduced recently in \cite{Br}, which is based on the Schur complement formula. In particular, our proof avoids the use of operator exponentials and is significantly simpler than \cite{ABS}.