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Quantum Chaos: Spectral Fluctuations and Overlap Distributions of the Three Level Lipkin-Meshkov-Glick Model


Meredith, Dawn Christine (1987) Quantum Chaos: Spectral Fluctuations and Overlap Distributions of the Three Level Lipkin-Meshkov-Glick Model. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7y5k-ex17.


We 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 quasichaotic 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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Koonin, Steven E.
Thesis Committee:
  • Koonin, Steven E. (chair)
  • Marcus, Rudolph A.
  • Simon, Barry M.
  • Wise, Mark B.
Defense Date:11 May 1987
Funding AgencyGrant Number
Record Number:CaltechTHESIS:02202019-120226199
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11406
Deposited On:22 Feb 2019 17:13
Last Modified:16 Apr 2021 22:12

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