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