A quasicrystal is an ordered but nonperiodic structure understood as a projection from a higher-dimensional periodic structure. Some physical properties of quasicrystals are different from those of conventional solids. An anomalous increase in heat capacity at high temperatures has been discussed for over two decades as a manifestation of a hidden high dimensionality of quasicrystals. A plausible candidate for this origin has been the phason, which has excitation modes originating from the additional atomic rearrangements introduced by the quasiperiodic order, which can be understood in terms of shifting a higher-dimensional lattice. However, most theoretical studies of phasons have used toy models. A theoretical study of the heat capacity of realistic quasicrystals or their approximants has yet to be conducted because of the huge computational complexity. To bridge this gap between experiment and theory, we show experiments and molecular simulations on the same material, an Al-Pd-Ru quasicrystal, and its approximants. We show that at high temperatures, aluminum atoms diffuse with discontinuouslike jumps, and the diffusion paths of the aluminum can be understood in terms of jumps corresponding to hyperatomic-fluctuations-associated atomic rearrangements of the phason degrees of freedom. It is concluded that the anomaly in the heat capacity of quasicrystals arises from the hyperatomic fluctuations that play a role in diffusive Nambu-Goldstone modes.

中文翻译：

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准晶体中的高温原子扩散和比热

准晶体是一种有序但非周期性的结构，被理解为高维周期性结构的投影。准晶体的一些物理性质与常规固体不同。二十多年来，人们一直在讨论高温下热容的异常增加，作为准晶体隐藏的高维性的表现。这种起源的一​​个可能的候选者是相子，它的激发模式源自准周期顺序引入的额外原子重排，这可以从移动高维晶格的角度来理解。然而，大多数相子理论研究都使用玩具模型。由于计算复杂性巨大，尚未对现实准晶体或其近似物的热容进行理论研究。为了弥合实验和理论之间的差距，我们展示了对同一材料（Al-Pd-Ru 准晶体及其近似材料）的实验和分子模拟。我们表明，在高温下，铝原子以不连续的跳跃方式扩散，并且铝的扩散路径可以用与超原子涨落相关的相子自由度原子重排相对应的跳跃来理解。结论是准晶体热容的异常是由在扩散南部-戈德斯通模式中起作用的超原子涨落引起的。