论文标题
Skyrmions的Smörgåsbord
A Smörgåsbord of Skyrmions
论文作者
论文摘要
我们研究带有锥度质量的标准Skyrme模型的静态溶液。使用大约$ 10^5 $伪随机的初始配置，由非对称产品Ansatz中的单个天空制成，并自动检测重复解决方案，我们发现了409个局部能量最小化器（Skyyrmions），该模型的Baryon数字1至16个模型为1至16，其中383个是新的。特别是，我们发现了Baryon数字5、8、9、10、11、12、13、14、15和16的新解决方案。我们每个Baryon数量的解决方案数量的结果表明，该数字可以多数序或指数增长。我们确定了新的解决方案家族：同步和反同步的六边形层中的天空片（我们称为石墨烯）； 2和3托里的链；链状解决方案包含铰链和许多聚集的天空。与普通传说相反，只有$ b = 12 $全球能量最小化器是由α颗粒或一块立方晶体制成的，而$ b = 9,11,14,15 $的最小化器包含$ b = 7 $ iCosahedrally Symmetrics Skyrmion作为组件。 $ b = 10,13,16 $是对称石墨烯般的解决方案。我们发现$ b = 5 $和$ b = 8 $的最小化器具有数值无法区分的能量。 $ b = 8 $候选者是两个立方体的链，这是立方Skyrme Crystal的一部分和最初由理性地图近似最初发现的富勒烯型球。 $ b = 5 $全局最小化器是众所周知的$ d_ {2d} $对称富勒烯或新的$ c_ {2v} $对称解决方案。最后，我们的发现显示大量解决方案没有离散的对称性或仅一个对称性，这与普通的传说是高度对称配置。
We study static solutions of the standard Skyrme model with a pion mass. Using approximately $10^5$ pseudo-random initial configurations made of single Skyrmions in the non-symmetrized product Ansatz and an automatic detection of repeated solutions, we find 409 local energy minimizers (Skyrmions) of the model with baryon numbers 1 through 16, of which 383 are new. In particular, we find new solutions for baryon numbers 5, 8, 9, 10, 11, 12, 13, 14, 15, and 16. Our results for the number of solutions per baryon number suggest that this number could grow either polynomially or exponentially. We identify new families of solutions: sheets of Skyrmions in synchronized and antisynchronized hexagonal layers (which we call graphene); chains of 2- and 3-tori; chain-like solutions containing a hinge and many clustered Skyrmions. Contrary to common lore, only the $B=12$ global energy minimizer is made of alpha particles or some chunk of a cubic crystal, whereas the $B=9,11,14,15$ minimizers contain the $B=7$ icosahedrally symmetric Skyrmion as a component. The $B=10,13,16$ are symmetric graphene-like solutions. We find $B=5$ and $B=8$ minimizers with numerically indistinguishable energies. The $B=8$ candidates are the chain of two cubes, which is a chunk of the cubic Skyrme crystal and the fullerene-type ball found originally by the rational map approximation. The $B=5$ global minimizer is either the well-known $D_{2d}$ symmetric fullerene or a new $C_{2v}$ symmetric solution. Finally, our findings show a large number of solutions have no discrete symmetries or just one symmetry, contrary to the common lore that Skyrmions are highly symmetric configurations.
