Origin of chaos in the spherical nuclear shell model: role of symmetries

Abstract

To elucidate the mechanism by which chaos is generated in the shell model, we compare three random-matrix ensembles: the Gaussian orthogonal ensemble, French's two-body embedded ensemble, and the two-body random ensemble (TBRE) of the shell model. Of these, the last two take account of the two-body nature of the residual interaction, and only the last, of the existence of conserved quantum numbers like spin, isospin, and parity. While the number of independent random variables decreases drastically as we follow this sequence, the complexity of the (fixed) matrices which support the random variables, increases even more. In that sense we can say that in the TBRE, chaos is largely due to the existence of (an incomplete set of) symmetries.

arXiv comment21 pages, 3 ps-figures. Revised version to appear in Nucl. Phys. A. New text and figures added

References in corpus (7)

• Quantum Monte Carlo Calculations of Light Nuclei
• Review of the k-Body Embedded Ensembles of Gaussian Random Matrices
• Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices
• Non-Universal Behavior of the k-Body Embedded Gaussian Unitary Ensemble of Random Matrices
• Distribution of spectral widths and preponderance of spin-0 ground states in nuclei
• Statistics of 2+ Levels in Even-Even Nuclei
• Spectral statistics of the k-body random-interaction model

Cited by in corpus (9)

• Random Matrices and Chaos in Nuclear Physics
• Random Matrices and Chaos in Nuclear Spectra
• Predominance of Prolate Nuclear Deformations Emerging from Many-Body Interactions
• The Two-Body Random Ensemble in Nuclei
• Quantum phase transitions and collective enhancement of level density in odd-A and odd-odd nuclei
• Nuclear Masses, Chaos, and the Residual Interaction
• Loschmidt echoes in two-body random matrix ensembles
• Random Matrix Ensembles For Many-Body Quantum Systems
• Random matrix ensembles with random interactions: Results for EGUE(2)-SU(4)