Existence and Vanishing of the Breathing Mode in Strongly Correlated Finite Systems

TL;DR

This paper investigates the conditions under which the breathing mode exists in finite strongly correlated systems, showing it only occurs under specific potentials or symmetries, and explores implications of its vanishing.

Contribution

It provides a general analysis of the existence and disappearance of the breathing mode in finite systems with various interaction potentials and symmetries.

Findings

Breathing mode exists only for specific potentials or symmetries.

Deviations from the breathing mode are demonstrated in Lennard-Jones and Yukawa systems.

Vanishing of the breathing mode leads to multiple monopole oscillations.

Abstract

One of the fundamental eigenmodes of finite interacting systems is the mode of {\em uniform radial expansion and contraction} -- the ``breathing'' mode (BM). Here we show in a general way that this mode exists only under special conditions: i) for harmonically trapped systems with interaction potentials of the form $1/r^\gamma$ $(\gamma\in\mathbb{R}_{\neq0})$ or $\log(r)$, or ii) for some systems with special symmetry such as single shell systems forming platonic bodies. Deviations from the BM are demonstrated for two examples: clusters interacting with a Lennard-Jones potential and parabolically trapped systems with Yukawa repulsion. We also show that vanishing of the BM leads to the occurence of multiple monopole oscillations which is of importance for experiments.