Level spacings for harmonic-oscillator systems

Akhilesh Pandey and Ramakrishna Ramaswamy
Phys. Rev. A 43, 4237 – Published 1 April 1991
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Abstract

From the viewpoint of eigenvalue level statistics, harmonic-oscillator systems are unusual. Although integrable, these systems are nongeneric, and a spacing distribution does not exist even as the number of levels N→∞. The origins of this pathological behavior are explored using methods of number theory and ergodic analysis. However, such nongenericity is extremely fragile, and the smallest nonlinearity asymptotically restores generic behavior. These results are of relevance to the study of molecular spectra, as well as to the quasienergy spectra of integrable quantum maps.

  • Received 14 August 1990

DOI:https://doi.org/10.1103/PhysRevA.43.4237

©1991 American Physical Society

Authors & Affiliations

Akhilesh Pandey

  • School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India

Ramakrishna Ramaswamy

  • Division of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444, Japan

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Issue

Vol. 43, Iss. 8 — April 1991

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