We build an effective field theory (EFT) for quasicrystals -- aperiodic incommensurate lattice structures -- at finite temperature, entirely based on symmetry arguments and a well-define action principle. By means of Schwinger-Keldysh techniques, we derive the full dissipative dynamics of the system and we recover the experimentally observed diffusion-to-propagation crossover of the phason mode. From a symmetry point of view, the diffusive nature of the phason at long wavelengths is due to the fact that the internal translations, or phason shifts, are symmetries of the system with no associated Noether currents. The latter feature is compatible with the EFT description only because of the presence of dissipation (finite temperature) and the lack of periodic order. Finally, we comment on the similarities with certain homogeneous holographic models and we formally derive the universal relation between the pinning frequency of the phonons and the damping and diffusion constant of the phason.

中文翻译：

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准晶体和相子动力学的有效场论

我们完全基于对称性论证和明确定义的作用原理，在有限温度下为准晶体-非周期性非对称晶格结构建立了有效的场论（EFT）。借助Schwinger-Keldysh技术，我们得出了系统的全部耗散动力学，并且我们恢复了实验观察到的相子模式的扩散-传播交叉。从对称性的角度来看，长相波的扩散特性是由于以下事实：内部平移或相移是系统的对称性，没有相关的Noether电流。仅因为存在耗散（有限的温度）和缺乏周期性，后一个功能才与EFT描述兼容。最后，