Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Nature of order from random two-body interactions

Drożdż, S., Mariusz Wojcik

Published Jan 1, 2001• 9 citations
OpenAlex

Abstract

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.

Related papers

On the origin of order from random two-body interactions

Stanisław Drożdż, Mariusz Wojcik

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 $J$-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 $J$-sectors.

arXiv:nucl-th/0007045•Jul 18, 2000•3 citations

Orderly Spectra from Random Interactions

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

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.

arXiv:nucl-th/9802066•Physical Review Letters•Mar 30, 1998•161 citations

Two-Body Random Ensembles: From Nuclear Spectra to Random Polynomials

Dimitri Kusnezov

The two-body random ensemble for a many-body bosonic theory is mapped to a problem of random polynomials on the unit interval. In this way one can understand the predominance of 0(+) ground states, and analytic expressions can be derived for distributions of lowest eigenvalues, energy gaps, density of states, and so forth. Recently studied nuclear spectroscopic properties are addressed.

arXiv:nucl-th/0009076•Physical Review Letters•Oct 30, 2000•37 citations

Order out of chaos in the shell model

Calvin W. Johnson

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.

AIP conference proceedings•Jan 1, 2000•0 citations

Spin structure of many-body systems with two-body random interactions

Lev Kaplan, T. Papenbrock, Calvin W. Johnson

We investigate the spin structure of many-fermion systems with a spin-conserving two-body random interaction. We find a strong dominance of spin-0 ground states and considerable correlations between energies and wave functions of low-lying states with different spin, but no indication of pairing. The spectral densities exhibit spin-dependent shapes and widths, and depend on the particle density as well as on the relative strengths of the spin-0 and spin-1 couplings in the two-body random matrix. The spin structure of low-lying states can largely be explained analytically.

arXiv:nucl-th/0007013•Physical Review C•Dec 15, 2000•33 citations

Emergence of Symmetry from Random n -Body Interactions

Alexander Volya

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.

arXiv:0712.3754•Physical Review Letters•Apr 22, 2008•14 citations
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.
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.
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.
We investigate the spin structure of many-fermion systems with a spin-conserving two-body random interaction. We find a strong dominance of spin-0 ground states and considerable correlations between energies and wave functions of low-lying states with different spin, but no indication of pairing. The spectral densities exhibit spin-dependent shapes and widths, and depend on the particle density as well as on the relative strengths of the spin-0 and spin-1 couplings in the two-body random matrix. The spin structure of low-lying states can largely be explained analytically.
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.