Merge pull request #1469 from julient31/pppm_spin (daa53e30) · Commits · 郑智淋 / lammps

doc/src/Eqs/pair_spin_dipole.jpg

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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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Original line number	Diff line number	Diff line
		\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}

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+15.6 KiB

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