# Stability of particles in two-dimensional quasicrystals against phasonic perturbations

## TL;DR

This paper studies how particles in two-dimensional quasicrystals respond to phasonic perturbations, identifying which particles are prone to flips and how fluctuations influence stability.

## Contribution

It introduces a method to determine particle stability against phasonic displacements and maps particles to predict flip susceptibility in quasicrystals.

## Key findings

- Particles near characteristic area edges are more prone to flips.
- Particles in the center are stable against phasonic fluctuations.
- The approach aids in understanding thermal effects in quasicrystals.

## Abstract

We investigate particles in two-dimensional quasicrystalline interference patterns and present a method to determine for each particle at which phasonic displacement a phasonic flip occurs. By mapping all particles into characteristic areas of reduced phononic and phasonic displacements, we identify the particles that are close to edges of these areas and can easily flip. In contrast, the particles in the center are hardly affected by phasonic fluctuations. Our results are important e.g. for light-induced colloidal structures or cold atomic gases in laser traps. In addition, our approach can help to predict how thermal fluctuations induce phasonic flips in intrinsic quasicrystals with structures close to interference patterns.