Effects of symmetry breaking in finite quantum systems

TL;DR

This review explores how symmetry breaking manifests uniquely in finite quantum systems, highlighting phenomena like crossover transitions and shape symmetry changes, with implications for understanding mesoscopic systems such as quantum dots and atomic nuclei.

Contribution

It emphasizes the peculiarities of symmetry breaking in finite systems, analyzing common properties across different physical systems and their spectral manifestations.

Findings

Symmetry breaking can be asymptotic or sharp depending on particle number.

Finite systems exhibit unique symmetry transformations like shape change.

Spectral features reveal symmetry breaking effects in mesoscopic systems.

Abstract

The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose-Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.