Effective Field Theory for Quasicrystals and Phasons Dynamics

TL;DR

This paper develops an effective field theory for quasicrystals at finite temperature, capturing the dissipative dynamics of phasons and explaining their diffusion-to-propagation crossover through symmetry and dissipation considerations.

Contribution

It introduces a symmetry-based EFT for quasicrystals that incorporates dissipation and derives the phason dynamics, including the diffusion-to-propagation crossover.

Findings

Derived the full dissipative phason dynamics using Schwinger-Keldysh techniques.

Revealed the symmetry origin of the diffusive nature of phasons.

Established a universal relation between phonon pinning frequency and phason damping.

Abstract

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.