Unverified Commit daa53e30 authored by Axel Kohlmeyer's avatar Axel Kohlmeyer Committed by GitHub
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Merge pull request #1469 from julient31/pppm_spin

Adding PPPM and Ewald solvers for electric dipoles and magnetic spins
parents 0b25d2fe 7a33d1e3
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+37.5 KiB
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+42 −0
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\documentclass[preview]{standalone}
\usepackage{varwidth}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath,amssymb,graphics,bm,setspace}

\begin{document}
\begin{varwidth}{50in}
  \begin{equation}
    \mathcal{H}_{\rm long}= 
    -\frac{\mu_{0} \left( \mu_B\right)^2}{4\pi} 
    \sum_{i,j,i\neq j}^{N}
    \frac{g_i g_j}{r_{ij}^3}
    \Big(3 
    \left(\bm{e}_{ij}\cdot \bm{s}_{i}\right) 
    \left(\bm{e}_{ij}\cdot \bm{s}_{j}\right) 
    -\bm{s}_i\cdot\bm{s}_j \Big)
    \nonumber
  \end{equation}
  \begin{equation}
    \bm{\omega}_i = 
    \frac{\mu_0 (\mu_B)^2}{4\pi\hbar}\sum_{j}
    \frac{g_i g_j}{r_{ij}^3}
    \, \Big(
    3\,(\bm{e}_{ij}\cdot\bm{s}_{j})\bm{e}_{ij}
    -\bm{s}_{j} \Big) \nonumber
  \end{equation}
  \begin{equation}
    \bm{F}_i =
    \frac{3\, \mu_0 (\mu_B)^2}{4\pi} \sum_j
    \frac{g_i g_j}{r_{ij}^4}
    \Big[\big( (\bm{s}_i\cdot\bm{s}_j) 
    -5(\bm{e}_{ij}\cdot\bm{s}_i)
    (\bm{e}_{ij}\cdot\bm{s}_j)\big) \bm{e}_{ij}+
    \big(
    (\bm{e}_{ij}\cdot\bm{s}_i)\bm{s}_j+
    (\bm{e}_{ij}\cdot\bm{s}_j)\bm{s}_i
    \big)
    \Big]
    \nonumber
  \end{equation}
\end{varwidth}
\end{document}
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\documentclass[preview]{standalone}
\usepackage{varwidth}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath,amssymb,graphics,bm,setspace}

\begin{document}
\begin{varwidth}{50in}
  \begin{equation}
    \mathcal{H}_{\rm long}= 
    -\frac{\mu_{0} \left( \mu_B\right)^2}{4\pi} 
    \sum_{i,j,i\neq j}^{N}
    \frac{g_i g_j}{r_{ij}^3}
    \Big(3 
    \left(\bm{e}_{ij}\cdot \bm{s}_{i}\right) 
    \left(\bm{e}_{ij}\cdot \bm{s}_{j}\right) 
    -\bm{s}_i\cdot\bm{s}_j \Big)
    \nonumber
  \end{equation}
\end{varwidth}
\end{document}
+15.6 KiB
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