Manu: saving work

Response_Letter/Response_Letter.tex

@@ -185,8 +185,13 @@ that the deviation from linearity of the ensemble energy would be zero.}
 	{Fig. 2: Why does the crossover point for the 1st excitation curves disappear for $L=8\pi$? }
 	\\
 	\alert{The legend of Fig.~2 was incorrect (the curves were mislabeled), but this has now been corrected.
-	In the new Fig.~2 (which is now Fig.~4 in the revised manuscript), this crossover has disappeared and the discussion is much more fluid:
-	when the weight of a state increases, this state is stabilized while the two others increases in energy (as it should).
+	In the corrected Fig.~2 (which is now Fig.~4 in the revised
+manuscript), the crossover point occurs for two different states that
+belong to two different ensembles. In other words, this point is not
+interesting anymore. The discussion of this Figure has become much more fluid:
+	when the weight of a state increases, this state is stabilized
+while the two others increase in energy (as it should). \manu{Well, the
+energy of the first excited state still decreases when $w_2$ increases}
 	The discussion regarding this figure has been modified accordingly.}
 %	\alert{It is clear from our derivations that the individual
 %correlation energies should vary with both the density {\it