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arXiv:nucl-th/0103069

Spin ordering of nuclear spectra from random interactions

Declan Mulhall, V. G. Zelevinsky, Alexander Volya

Published Mar 27, 2001• 0 citations
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Abstract

Recent developments in many-body quantum chaos have raised the issue of correlations between different families of levels in the spectra of random fermionic systems. It seems that rotational invariance is sufficient to force an otherwise random system to have statistically ordered spectra where the ground state can have zero spin or the maximum spin allowed a huge portion of the time. We have tackled this question and have characterized the role of ``geometric chaoticity'' and pairing in random systems. We have shown how the geometry gives rise to such a distribution of ground state spins and examined the coexistence of these regularities with chaotic wave functions.

DOI
10.48550/arxiv.nucl-th/0103069

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Recent developments in many-body quantum chaos have raised the issue of correlations between different families of levels in the spectra of random fermionic systems. It seems that rotational invariance is sufficient to force an otherwise random system to have statistically ordered spectra where the ground state can have zero spin or the maximum spin allowed a huge portion of the time. We have tackled this question and have characterized the role of ``geometric chaoticity'' and pairing in random systems. We have shown how the geometry gives rise to such a distribution of ground state spins and examined the coexistence of these regularities with chaotic wave functions.
Recent developments in many-body quantum chaos show that a quantum system with strong incoherent interactions can still be described with the aid of mean quasiparticle occupation numbers as in Fermi liquid theory. We use these ideas and the geometric chaoticity of angular momentum coupling to explain the predominance of ground states with zero spin and the maximum possible spin for a system of randomly interacting fermions in a rotationally invariant mean field (an analog of the Hund rule). We show that spin ordering coexists with the chaotic features of the ground-state wave functions.
Numerical simulations show that the ground state spin of a finite many-body system with random but rotationally invariant interactions is predominantly zero. This means that it is not sufficient to explain the zero ground state spin of even-even nuclei only by pairing correlations. Simple explanations based on a statistical multiplicity, width of the level density, effective pairing, formation of condensates etc. do not work. We suggest statistical theory based on the effective mean field and geometric chaoticity of angular momentum coupling of individual particles. The results show a significant role of symmetry arguments in finite systems.
Nuclei at low excitation energy exhibit such well-ordered behavior, such as rotational and vibrational bands as well as pairing gaps, that they are commonly described with algebraic models; but does such order originate in the details of the nuclear force, or are they emergent properties of dense fermion systems? To answer this, I consider ensembles of random two-body shell-model interactions and examine the low-lying spectra and wavefunctions. Some striking regularities emerge: in particular, pairing appears to be a ubiquitous phenomenon, even in the absence of explicit pairing interactions! These results are remarkably insensitive to the detailed definition of the ensemble.
The problem of random interactions leading to regular spectra in shell model type simulations is described. The key results are reviewed alnog with a selection of the explanations. A model system of N particles on 2 spin levels having random 2-body collisions that conserve angular momentum is examined. Preliminary results are described, including the ground state spin distributions peaked at extreme values of angular momentum, signatures of rotational bands, and smooth parabolic yrast lines. A simple random matrix theory analysis shows signatures of quantum chaos in the level spacing distribution and the Δ3 statistic.
An ensemble with random n-body interactions is investigated in the presence of symmetries. A striking emergence of regularities in the spectra, ground state spins, and isospins is discovered. In even-particle systems the strong preponderance of spin zero ground states is observed with three, four, and higher-order random many-body interactions, and similar trends are discovered in systems that possess both rotational and isospin symmetry. Various types of correlations from pairing to spectral sequences and correlations across different masses are explored. A search for an interpretation is presented.