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diff --git a/Jauslin_2023b.tex b/Jauslin_2023b.tex index 7d0ed74..d7ec6a3 100644 --- a/Jauslin_2023b.tex +++ b/Jauslin_2023b.tex @@ -283,6 +283,8 @@ where $P_{\mathbf k}^{(i)}$ is the projector onto the subspace in which the $i$- Thus, $N_{\kappa}$ is the integral over the sphere of radius $\kappa$ of the number of particles in the state $e^{i\mathbf k\mathbf x}$. In particular, $\eta=N_0/N$. (The momentum distribution is then defined as $\mathcal M(\kappa):=N_\kappa/(4\pi\kappa^2\rho)$, but, in the following, we shall show results for $N_\kappa$ instead.) +Computing $N_\kappa$ using the Simplified approach poses one difficulty: the projector $P_{\mathbf k}^{(i)}$ breaks the translation invariance of the system, which was, until recently, necessary for the derivation of the Simplified approach. +This problem has been resolved in\-~\cite{Ja23}, in which the Simplified approach is constructed in non-translation invariant settings. \bigskip \indent |