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摘要翻译：
我们导出了新的对偶关系，将一类软对势的位形能量与对应的对偶（傅里叶变换）势的能量联系起来。我们通过说明如何利用短程势的经典基态信息来得出关于长程势基态性质的新结论，反之亦然来应用它们。它们还导致了在相共存的密度区间内t=0系统能量的界限，一个表现出无穷多个“相变”的一维系统的识别，以及关于纯排斥单调势的基态的猜想。
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英文标题：
《New Duality Relations for Classical Ground States》
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作者：
S. Torquato and F. H. Stillinger
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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：
We derive new duality relations that link the energy of configurations associated with a class of soft pair potentials to the corresponding energy of the dual (Fourier-transformed) potential. We apply them by showing how information about the classical ground states of short-ranged potentials can be used to draw new conclusions about the nature of the ground states of long-ranged potentials and vice versa. They also lead to bounds on the T=0 system energies in density intervals of phase coexistence, the identification of a one-dimensional system that exhibits an infinite number of ``phase transitions," and a conjecture regarding the ground states of purely repulsive monotonic potentials.
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PDF链接：
https://arxiv.org/pdf/710.5315
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