Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime

For a translation invariant system of \(N\) bosons in the Gross-Pitaevskii regime, we establish a precise bound for the ground state energy \(E_N\). While the leading, order \(N\), contribution to \(E_N\) has been known since [30,28] and the second order corrections (of order one) have been first de...

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Published in:arXiv.org 2024-04
Main Authors: Caraci, Cristina, Olgiati, Alessandro, Diane Saint Aubin, Schlein, Benjamin
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Asymptotic series
Bosons
Ground state
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Olgiati, Alessandro
Diane Saint Aubin
Schlein, Benjamin
description For a translation invariant system of \(N\) bosons in the Gross-Pitaevskii regime, we establish a precise bound for the ground state energy \(E_N\). While the leading, order \(N\), contribution to \(E_N\) has been known since [30,28] and the second order corrections (of order one) have been first determined in [5], our estimate also resolves the next term in the asymptotic expansion of \(E_N\), which is of the order \((\log N) / N\).
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subjects Asymptotic series
Bosons
Ground state
title Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
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