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International Journal of Modern Physics B

MANY-BODY ASPECTS OF QUANTUM CHAOS

Vladimir Zelevinsky

Published Mar 10, 1999• 3 citations
Publisher

Abstract

Realistic many-body quantum systems with strong interaction reveal generic chaotic properties in level statistics and structure of eigenfunctions. In complex atoms and nuclei onset of chaos is driven by the residual interaction. We discuss specific features of many-body chaos in mesoscopic systems (complexity and thermalization; coexistence of chaos and collective motion; spreading widths of simple modes; geometric chaoticity).

DOI
10.1142/s0217979299000461

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Many-body quantum chaos results from interparticle interactions in mesoscopic systems at sufficiently high level density. A short review shows that, going beyond generic properties of local spectral statistics, the ideas of many-body quantum chaos serve as a rich source of new theoretical approaches, computational and experimental tools. Chosen examples include the enhancement of weak perturbations, thermalization in finite systems, exponential convergence of large Hamiltonian matrices and correlations between the states of different symmetry.
We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts are not chaotic. The spectrum of the first exhibits repulsion of the energy levels, which is one of the main signatures of quantum chaos. We show how level repulsion develops in one-dimensional systems of interacting spins 1/2 which are devoid of random elements and involve only two-body interactions. In addition to the statistics of the eigenvalues, we analyze how the structure of the eigenstates may indicate chaos. The programs used to obtain the data are available online.
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We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts are not chaotic. The spectrum of the first exhibits repulsion of the energy levels. This is one of the main signatures of quantum chaos. We show how level repulsion develops in one-dimensional systems of interacting spins 1/2 which are devoid of random elements and involve only two-body interactions. In addition to the statistics of the eigenvalues, we analyze how the structure of the eigenstates may indicate chaos. The programs used to obtain the data are available online.