软物质系统经典基态的对偶关系
Duality Relations for the Classical Ground States of Soft-Matter Systems
摘要：
有界相互作用在软物质体系中特别重要，如胶体、微乳液和聚合物。我们推导了一类软势的新的对偶关系，包括三体和高阶函数，可以应用于有序和无序的经典基态。这些对偶关系将与实空间势相关的组态能量与对偶（傅立叶变换）势的相应能量联系起来。我们应用的对偶关系，演示如何信息的经典基态的短程电位可以用来得出新的结论，基态的长程电位，反之亦然。的对偶关系也导致界限的T=0系统的能量在密度区间的相共存。此外，我们确定类的“自相似”的潜力，其中一个可以涉及低和高密度基态能量。我们分析的基态配置和热力学性质的一维系统以前被认为表现出无限数量的结构相变和评论已知的基态的纯排斥单调的潜力在我们的对偶关系的背景下。
英文摘要：
Bounded interactions are particularly important in soft-matter systems, such as colloids, microemulsions, and polymers. We derive new duality relations for a class of soft potentials, including three-body and higher-order functions, that can be applied to ordered and disordered classical ground states. These duality relations link the energy of configurations associated with a real-space potential to the corresponding energy of the dual (Fourier-transformed) potential. We apply the duality relations by demonstrating how information about the classical ground states of short-ranged potentials can be used to draw new conclusions about the ground states of long-ranged potentials and vice versa. The duality relations also lead to bounds on the T=0 system energies in density intervals of phase coexistence. Additionally, we identify classes of "self-similar" potentials, for which one can relate low- and high-density ground-state energies. We analyze the ground state configurations and thermodynamic properties of a one-dimensional system previously thought to exhibit an infinite number of structural phase transitions and comment on the known ground states of purely repulsive monotonic potentials in the context of our duality relations.
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