长程相互作用体系中的BCC晶格
The BCC lattice in a long range interaction system
摘要：
虽然六方晶格在二维中是普遍存在的，但体心立方晶格和面心晶格都通常在三维中观察到。由嵌段共聚物理论提出的几何变分问题由短程相互作用能和长程相互作用能组成。在三维情况下，当长程相互作用由非定域算符$(-Δ)^{-3/2}$给出时，证明了体心立方晶格是优选结构。
英文摘要：
While the hexagonal lattice is ubiquitous in two dimensions, the body centered cubic lattice and the face centered lattice are both commonly observed in three dimensions. A geometric variational problem motivated by the diblock copolymer theory consists of a short range interaction energy and a long range interaction energy. In three dimensions, and when the long range interaction is given by the nonlocal operator $(-Δ)^{-3/2}$, it is proved that the body centered cubic lattice is the preferred structure.
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