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| -rw-r--r-- | Giuliani_Jauslin_2015.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/Giuliani_Jauslin_2015.tex b/Giuliani_Jauslin_2015.tex index fd45555..65d8bd2 100644 --- a/Giuliani_Jauslin_2015.tex +++ b/Giuliani_Jauslin_2015.tex @@ -574,8 +574,8 @@ where $\mathcal H_0$ is the {\it free Hamiltonian} and $\mathcal H_I$ is the {\i \end{array}\label{hamx}\end{equation} Equation~(\ref{hamx}) can be rewritten in Fourier space as follows. We define the Fourier transform of the annihilation operators as \begin{equation} \hat a_{k}:=\sum_{x\in\Lambda}e^{ikx}a_{x}\;,\quad -\hat{\tilde b}_{k}:=\sum_{x\in\Lambda}e^{ikx}\hat{\tilde b}_{x+\delta_1}\;,\quad -\hat{\tilde a}_{k}:=\sum_{x\in\Lambda}e^{ikx}\hat{\tilde a}_{x-\delta_1}\;,\quad +\hat{\tilde b}_{k}:=\sum_{x\in\Lambda}e^{ikx}\tilde b_{x+\delta_1}\;,\quad +\hat{\tilde a}_{k}:=\sum_{x\in\Lambda}e^{ikx}\tilde a_{x-\delta_1}\;,\quad \hat b_{k}:=\sum_{x\in\Lambda}e^{ikx}b_{x+\delta_1}\;\end{equation} in terms of which \begin{equation} |