Thermal and Quantum Fluctuation Effects in Quasiperiodic Systems in External Potentials

TL;DR

This study investigates how thermal and quantum fluctuations influence the stability of quasiperiodic structures in many-body systems with specific pair interactions under harmonic confinement, revealing that such fluctuations tend to disrupt quasicrystalline order.

Contribution

It provides a detailed numerical analysis of the effects of thermal and quantum fluctuations on quasiperiodic phases in many-body systems with Lifshitz--Petrich--Gaussian interactions.

Findings

Fluctuations generally destroy quasicrystalline patterns.

Competition between harmonic confinement and interaction wavelengths affects structure stability.

Quantum effects can significantly alter the phase behavior.

Abstract

We analyze the many-body phases of an ensemble of particles interacting via a Lifshitz--Petrich--Gaussian pair potential in a harmonic confinement. We focus on specific parameter regimes where we expect decagonal quasiperiodic cluster arrangements. Performing classical Monte Carlo as well as path integral quantum Monte Carlo methods, we numerically simulate systems of a few thousand particles including thermal and quantum fluctuations. Our findings indicate that the competition between the intrinsic length scale of the harmonic oscillator and the wavelengths associated to the minima of the pair potential generically lead to a destruction of the quasicrystalline pattern. Extensions of this work are also discussed.