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author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-09 13:36:22 +0100 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2020-12-09 13:36:22 +0100 |
commit | d887e8a5178512e7c4f9d9d033d2560222e1ed24 (patch) | |
tree | c470793e4480498a0fe86df4b86d895ca419c40e | |
parent | 7300e6d6aaedb8ac603d2b955616e9b992ab18c6 (diff) | |
parent | d656e21ccf99590d88de7feab1fed7a4e6c38ffa (diff) | |
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Merge branch 'master' of https://git.overleaf.com/5fcce4736e7f601ffb7e1484
-rw-r--r-- | bezout.tex | 2 |
1 files changed, 1 insertions, 1 deletions
@@ -62,7 +62,7 @@ whose elements are complex normal with $\overline{|J|^2}=p!/2N^{p-1}$ and $\overline{J^2}=\kappa\overline{|J|^2}$ for complex parameter $|\kappa|<1$. The constraint becomes $z^2=N$. The motivations for this paper are of two types. On the practical side, there are situations in which complex variables -have in a disorder problem appear naturally: such is the case in which they are {\em phases}, as in random laser problems \cite{Antenucci_2015_Complex, etc}. Another problem where a Hamiltonian very close to ours has been proposed is the Quiver Hamiltonians \cite{Anninos_2016_Disordered} modeling Black Hole horizons in the zero-temperature limit. +have in a disorder problem appear naturally: such is the case in which they are {\em phases}, as in random laser problems \cite{Antenucci_2015_Complex}. Another problem where a Hamiltonian very close to ours has been proposed is the Quiver Hamiltonians \cite{Anninos_2016_Disordered} modeling Black Hole horizons in the zero-temperature limit. There is however a more fundamental reason for this study: we know from experience that extending a problem to the complex plane often uncovers an underlying simplicity that is hidden in the purely real case. Consider, for example, the procedure of starting from a simple, known Hamiltonian $H_{00}$ and studying $\lambda H_{00} + (1-\lambda H_{0} )$, evolving adiabatically from $\lambda=0$ to $\lambda=1$, as is familiar from quantum annealing. The $H_{00}$ is a polynomial of degree $p$ chosen to have simple, known roots. Because we are working in complex variables, and the roots are simple all the way (we shall confirm this), we may follow a root from $\lambda=0$ to $\lambda=1$. With real |