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Diffstat (limited to 'frsb_kac_new.tex')
| -rw-r--r-- | frsb_kac_new.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/frsb_kac_new.tex b/frsb_kac_new.tex index 99455de..f5e9422 100644 --- a/frsb_kac_new.tex +++ b/frsb_kac_new.tex @@ -400,9 +400,9 @@ Consider the extremum problem of \eqref{eq:diagonal.action} with respect to $R_d =-\frac12f'(1)+\frac12\frac1{R_d^2}\lim_{n\to0}\frac1n\operatorname{Tr}((D_d/R_d^2)Q+I)^{-1}Q \label{eq:saddle.d}\\ 0 &=\frac{\partial S}{\partial R_d} - =-\mu+\hat\epsilon f'(1)+R_df''(1)+\frac1{R_d}+\frac{D_d}{R_d}\lim_{n\to0}\frac1n\operatorname{Tr}((D_d/R_d^2)Q+I)^{-1}Q \label{eq:saddle.r} + =-\mu+\hat\epsilon f'(1)+R_df''(1)+\frac1{R_d}-\frac{D_d}{R_d^3}\lim_{n\to0}\frac1n\operatorname{Tr}((D_d/R_d^2)Q+I)^{-1}Q \label{eq:saddle.r} \end{align} -Adding $2(D_d/R_d)$ of \eqref{eq:saddle.d} to \eqref{eq:saddle.r} and multiplying by $R_d$ gives +Adding $2(D_d/R_d)$ times \eqref{eq:saddle.d} to \eqref{eq:saddle.r} and multiplying by $R_d$ gives \begin{equation} 0=-R_d\mu+1+R_d^2f''(1)+f'(1)(R_d\hat\epsilon-D_d) \end{equation} |