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| author | Ian Jauslin <ian.jauslin@rutgers.edu> | 2023-02-28 16:12:24 -0500 |
|---|---|---|
| committer | Ian Jauslin <ian.jauslin@rutgers.edu> | 2023-02-28 16:12:24 -0500 |
| commit | 6bb2f5a429edbc41749c61f6f962654336909ba6 (patch) | |
| tree | cd2615b557faf8fc14a79c898b6120097a30f304 | |
| parent | 7f0a6766b9a471796a8adcfca847a926cdbe5c97 (diff) | |
| -rw-r--r-- | Jauslin_2023.tex | 7 | ||||
| -rw-r--r-- | bibliography/bibliography.tex | 3 |
2 files changed, 10 insertions, 0 deletions
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 diff --git a/bibliography/bibliography.tex b/bibliography/bibliography.tex index 2419e95..ca6105f 100644 --- a/bibliography/bibliography.tex +++ b/bibliography/bibliography.tex @@ -51,6 +51,9 @@ arxiv:{\tt\color{blue}\href{https://arxiv.org/abs/2203.03440}{2203.03440}}.\par\ \bibitem[Ja22]{Ja22}I. Jauslin - {\it Review of a Simplified Approach to study the Bose gas at all densities}, The Physics and Mathematics of Elliott Lieb, The\-~90th Anniversary Volume I, chapter\-~25, pages\-~609-635, ed. Rupert L. Frank, Ari Laptev, Mathieu Lewin, Robert Seiringer, EMS Press, 2022,\par\penalty10000 doi:{\tt\color{blue}\href{http://dx.doi.org/10.4171/90-1/25}{10.4171/90-1/25}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2202.07637}{2202.07637}}.\par\medskip +\bibitem[Ja23]{Ja23b}I.\-~Jauslin - {\it Evidence of a liquid phase in interacting Bosons at intermediate densities}, arXiv preprint, 2023\par\penalty10000 +arxiv:{\tt\color{blue}\href{https://arxiv.org/abs/2302.13449}{2302.13449}}.\par\medskip + \bibitem[LHY57]{LHY57}T.D. Lee, K. Huang, C.N. Yang - {\it Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties}, Physical Review, volume\-~106, issue\-~6, pages\-~1135-1145, 1957,\par\penalty10000 doi:{\tt\color{blue}\href{http://dx.doi.org/10.1103/PhysRev.106.1135}{10.1103/PhysRev.106.1135}}.\par\medskip |