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Miguel A. L. Marques edited Magnetic response.tex
over 9 years ago
Commit id: 2cc9e9d95818cc668127e67c2e2a7d3c67e16d9c
deletions | additions
diff --git a/Magnetic response.tex b/Magnetic response.tex
index 78c03fa..d327ca1 100644
--- a/Magnetic response.tex
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\begin{equation}
\label{eq:iclmag2}
\delta^2\op{\vv}^{\mathrm{mag}} \delta^2V^{\mathrm{mag}} =
\frac1{8c^2}\left[(\vec{B}\times\op{{\vec{r}}})^2+
\sum_{\ia}\vec{R_\ia}\times\op{\vec{r}}\cdot\op{\vec{D}}_{\ia}^{\mathrm{nl}}\cdot\vec{B}\times\op{\vec{r}}\right]\ \frac1{8c^2}\left[(\vec{B}\times{\vec{r}})^2+
\sum_{l}\vec{R_l}\times \vec{r}\cdot\op{\vec{D}}_l^{\mathrm{nl}}\cdot\vec{B}\times\vec{r}\right]\ ,
\end{equation}
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with
\(\op{\vec{\vv}}_{\ia}^{\mathrm{nl}}=-i\left[{\vec{r}},\op{\vv}^{nl}_\ia\right]\) \(\vec{V}_{l}^{\mathrm{nl}}=-i\left[{\vec{r}},V^{nl}_l\right]\)
and
\({D}_{\ia\ii\ji}^{\mathrm{nl}}=-\left[{r}_\ii,\left[\op{r}_\ji,{\vv}^{nl}_{\ia}\right]\right]\),
where \({\vv}^{nl}_\ia\) is the non-local potential associated to