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arXiv:nucl-th/9802066 · Physical Review Letters

Orderly Spectra from Random Interactions

Calvin W. Johnson, G. F. Bertsch, David J. Dean

Published Mar 30, 1998• 161 citations
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Abstract

We investigate the low-lying spectra of many-body systems with random two-body interactions, specifying that the ensemble be invariant under particle-hole conjugation. Surprisingly we find patterns reminiscent of more orderly interactions, such as a predominance of $J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ ground states separated by a gap from the excited states, and evidence of phonon vibrations in the low-lying spectra.

DOI
10.1103/physrevlett.80.2749

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We investigate the low-lying spectra of many-body systems with random two-body interactions, specifying that the ensemble be invariant under particle-hole conjugation. Surprisingly we find patterns reminiscent of more orderly interactions, such as a predominance of J=0J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0J=0 ground states separated by a gap from the excited states, and evidence of phonon vibrations in the low-lying spectra.
We investigate the origin of order in the low-lying spectra of many-body systems with random two-body interactions. Our study based both on analytical as well as on numerical arguments shows that except for the most J-stretched states, the ground states in the higher J-sectors are more orderly and develop larger energy gaps than the ones in the J=0-sector. Due to different characteristic energy scales in different J-sectors the J=0 ground states may predominate only when all the states are taken together.
We investigate the origin of order in the low-lying spectra of many-body systems with random two-body interactions. Contrary to the common belief our study based both on analytical as well as on numerical arguments shows that these are the higher JJJ-sectors whose ground states are more orderly than the ones in the J=0-sector. A predominance of J=0 ground states turns out to be the result of putting on together states with different characteristic energy scales from different JJJ-sectors.
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.
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