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Properties of vibrational energy levels in the quasi periodic and stochastic regimes

Noid, D. W. and Koszykowski, M. L. and Tabor, M. and Marcus, R. A. (1980) Properties of vibrational energy levels in the quasi periodic and stochastic regimes. Journal of Chemical Physics, 72 (11). pp. 6169-6175. ISSN 0021-9606. http://resolver.caltech.edu/CaltechAUTHORS:NOIjcp80a

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Abstract

Several aspects of the quantal energy spectrum are explored for the Henon–Heiles Hamiltonian system: a striking and initially unexpected continuation of sequences of eigenvalues from the quasiperiodic to the stochastic regime, the origin of large second differences Delta2Ei of eigenvalues arising from variation of a parameter, the comparison of classical and quantal spectra, and a comparison of the "classical" and quantal number of states. In the study of the second differences we find both "crossings" and "avoided crossings" of the eigenvalues. We discuss the importance of overlapping avoided crossings as a basis for a possible theory of "quantum stochasticity".


Item Type:Article
Additional Information:Copyright © 1980 American Institute of Physics. (Received 8 January 1980; accepted 15 February 1980) One of us (D.W.N.) was supported by a Wigner Fellowship for ORNL. The research was sponsored by the U.S. Department of Energy under Contract W-7405-eng-26 with the Union Carbide Corporation (at Oak Ridge), the Department of Energy (at Sandia National Laboratories) and the National Science Foundation (at the California Institute of Technology). Research supported by D.O.E. and N.S.F. Arthur Amos Noyes Laboratory of Chemical Physics, Contribution No. 6157 from the California Institute of Technology.
Subject Keywords:HAMILTONIAN FUNCTION, VIBRATIONAL STATES, STOCHASTIC PROCESSES, EIGENVALUES, QUANTUM MECHANICS
Record Number:CaltechAUTHORS:NOIjcp80a
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:NOIjcp80a
Alternative URL:http://dx.doi.org/10.1063/1.439075
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10940
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:19 Jun 2008
Last Modified:26 Dec 2012 10:06

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