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Diffstat (limited to 'frsb_kac_new.tex')
| -rw-r--r-- | frsb_kac_new.tex | 6 |
1 files changed, 5 insertions, 1 deletions
diff --git a/frsb_kac_new.tex b/frsb_kac_new.tex index 552ee9b..e1c5768 100644 --- a/frsb_kac_new.tex +++ b/frsb_kac_new.tex @@ -295,7 +295,11 @@ Introducing the parameters: \begin{aligned} \mathcal D(\mu) &=\frac1N\overline{\log|\det(\partial\partial H(s_a)+\mu I)|} - =\int d\lambda\,\rho(\lambda+\mu)\log|\lambda| + =\int d\lambda\,\rho(\lambda+\mu)\log|\lambda| \\ + &=\operatorname{Re}\left\{ + \frac12\left(1+\frac\mu{2f''(1)}\left(\mu\pm\sqrt{\mu^2-4f''(1)}\right)\right) + -\log\left(\frac1{2f''(1)}\left(\mu\pm\sqrt{\mu^2-4f''(1)}\right)\right) + \right\} \end{aligned} \end{equation} |