摘要翻译:
弯曲基片上的近晶级可以用秩一微分形式(1-形式)来描述,其几何意义是密度调制局部相场的微分。1型的外导数是局域位错密度。弹性变形用精确微分形式的叠加来描述。用这种形式研究环面和球面上的近晶序,我们发现这两个体系都表现出许多拓扑上不同的低能态,这些低能态可以用两个整数拓扑电荷来表征。低能态的总数以衬底面积的平方根为尺度。对于球体上的近晶,我们还探讨了作为可能的低能激发的离解运动,以及它的拓扑含义。
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英文标题:
《Topology of Smectic Order on Compact Substrates》
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作者:
Xiangjun Xing (Syracuse University)
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最新提交年份:
2008
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分类信息:
一级分类:Physics 物理学
二级分类:Soft Condensed Matter 软凝聚态物质
分类描述:Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜,聚合物,液晶,玻璃,胶体,颗粒物质
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一级分类:Physics 物理学
二级分类:Statistical Mechanics 统计力学
分类描述:Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变,热力学,场论,非平衡现象,重整化群和标度,可积模型,湍流
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英文摘要:
Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. Applying this formalism to study smectic order on torus as well as on sphere, we find that both systems exhibit many topologically distinct low energy states, that can be characterized by two integer topological charges. The total number of low energy states scales as the square root of the substrate area. For smectic on a sphere, we also explore the motion of disclinations as possible low energy excitations, as well as its topological implications.
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PDF链接:
https://arxiv.org/pdf/708.3182