From c8f071589950b388fde16d0926a61410fc51766e Mon Sep 17 00:00:00 2001 From: Ian Jauslin Date: Sun, 11 Sep 2016 23:42:37 +0000 Subject: Typo in definition of Fourier transform --- Giuliani_Jauslin_2015.tex | 4 ++-- 1 file 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} -- cgit v1.2.3-54-g00ecf