关于非单调势的晶格六方结晶

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Senping Luo, Juncheng Wei
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引用次数: 0

摘要

我们证明,对于α≥1,在二维单位密度晶格中,minL∑P∈L(|P|2-β)e-πα|P|2在β≤12πα的六边形晶格中实现,而在β>12πα中不存在。这里具有单位密度的六方格可表示为Λ1=132[Z(1,0)⊕Z(12,32)]。由此引出以下两个应用。(1) 假设 α ≥ 1。那么,在 2d 单位密度晶格中,六边形晶格可实现 minL∑P∈L|P|2e-πα|P|2 。(2) 假设 β > α ≥ 1。那么对于 b≤βα,minz∈Hθ(α;z)-bθ(β;z)在 z=eiπ3(对应于六方格)处实现,而对于 b>βα 则不存在。这里的 θ(α; z) 是二维 Theta 函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On lattice hexagonal crystallization for non-monotone potentials
We prove that for α ≥ 1, among 2d unit density lattices, minL∑P∈L(|P|2−β)e−πα|P|2 is achieved at hexagonal lattice for β≤12πα and does not exist for β>12πα. Here the hexagonal lattice with unit density can be expressed by Λ1=132[Z(1,0)⊕Z(12,32)]. This leads to two applications as follows. (1) Assume that α ≥ 1. Then, among 2d unit density lattices, minL∑P∈L|P|2e−πα|P|2 is achieved at hexagonal lattice. (2) Assume that β > α ≥ 1. Then minz∈Hθ(α;z)−bθ(β;z) is achieved at z=eiπ3 (corresponding to hexagonal lattice) for b≤βα and does not exist for b>βα. Here θ(α; z) is the two-dimensional Theta function.
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来源期刊
Journal of Mathematical Physics
Journal of Mathematical Physics 物理-物理:数学物理
CiteScore
2.20
自引率
15.40%
发文量
396
审稿时长
4.3 months
期刊介绍: Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.
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