Random Matrices and Chaos in Nuclear Physics

TL;DR

This paper reviews how random-matrix theory explains spectral fluctuations and chaos in nuclear physics, highlighting its broad applicability across various nuclear models and ensembles, with exceptions in certain deformed nuclei.

Contribution

It provides a comprehensive survey of experimental and theoretical evidence supporting chaos in nuclear spectra using random-matrix theory.

Findings

Spectral fluctuations in nuclei align with random-matrix predictions.

Chaos is prevalent in nuclear spectra, except in ground states of strongly deformed nuclei.

Various nuclear models exhibit signatures of quantum chaos consistent with random-matrix theory.

Abstract

The authors review the evidence for the applicability of random--matrix theory to nuclear spectra. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately: quantum chaos) in nuclei whenever random--matrix predictions are fulfilled. An introduction into the basic concepts of random--matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random--matrix ensembles patterned after the shell model such as the embedded two--body ensemble, the two--body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground--state regions of strongly deformed nuclei.