Quantum chaos: spectral fluctuations and overlap distributions of the three level Lipkin-Meshkov-Glick model

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1987

OSTI ID:5644443

Meredith, D C

The author test the prediction that quantum systems with chaotic classical analogs have spectral fluctuations and overlap distributions equal to those of the Gaussian Orthogonal Ensemble (GOE). The subject of our study is the three level Lipkin-Meshkov-Glick model of nuclear physics. This model differs from previously investigated systems because the quantum basis and classical phase space are compact, and the classical Hamiltonian has quartic momentum dependence. We investigate the dynamics of the classical analog to identify values of coupling strength and energy ranges for which the motion is chaotic, quasi-chaotic, and quasi-integrable. We then analyze the fluctuation properties of the eigenvalues for those same energy ranges and coupling strength, and we find that the chaotic eigenvalues are in good agreement with GOE fluctuations, while the quasi-integrable and quasi-chaotic levels fluctuations are closer to the Poisson fluctuations that are predicted for integrable systems. We also study the distribution of the overlap of a chaotic eigenvector with a basis vector, and find that in some cases it is a Gaussian random variable as predicted by GOE. This result, however, is not universal.

• Research Organization: California Inst. of Tech., Pasadena (USA)
• OSTI ID: 5644443
• Country of Publication: United States
• Language: English

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