From 6bb2f5a429edbc41749c61f6f962654336909ba6 Mon Sep 17 00:00:00 2001
From: Ian Jauslin <ian.jauslin@rutgers.edu>
Date: Tue, 28 Feb 2023 16:12:24 -0500
Subject: Add acknowledgements and reference to [Ja23]

---
 Jauslin_2023.tex | 7 +++++++
 1 file changed, 7 insertions(+)

(limited to 'Jauslin_2023.tex')

diff --git a/Jauslin_2023.tex b/Jauslin_2023.tex
index c813122..e2a31b0 100644
--- a/Jauslin_2023.tex
+++ b/Jauslin_2023.tex
@@ -80,6 +80,7 @@ The {\it condensate fraction} is defined as the proportion of particles in the c
 The momentum distribution is an extension of the condensate fraction to a more general family of states.
 In particular, computing $\mathcal M(k)$ for $k\neq 0$ amounts to counting particles that are {\it not} in the condensate.
 This quantity has been used in the recent proof\-~\cite{FS20,FS22} of the energy asymptotics of the Bose gas at low density.
+A numerical computation of the prediction of the Simplified approach for $\mathcal M(k)$ have been published in\-~\cite{Ja23b}.
 \bigskip
 
 \indent
@@ -1690,6 +1691,12 @@ so by\-~(\ref{erho}),
 This, together with\-~(\ref{final1}), implies\-~(\ref{Msimpleqbog}).
 \qed
 
+\bigskip
+\bigskip
+
+\hfil{\bf Acknowledgements}\par
+The author thanks Elliott H. Lieb, Eric A. Carlen and Markus Holzmann for many valuable discussions.
+The author acknowledges support from the Simons Foundation, Grant Number\-~825876.
 
 \vfill
 \eject
-- 
cgit v1.2.3-70-g09d2

