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Small denominators, frequency operators, and Lie transforms for nearly integrable quantum spin systems

Gramespacher, Thomas and Weigert, S. (1996) Small denominators, frequency operators, and Lie transforms for nearly integrable quantum spin systems. Physical Review A. pp. 2971-2982. ISSN 1050-2947

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Abstract

Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting. They are conceptually useful because another formulation can be given to unitary perturbation theory. When worked out for quantum spin systems, this variant is found to be formally equivalent to canonical perturbation theory applied to nearly integrable systems consisting of classical spins. In particular, it becomes possible to locate the quantum-mechanical operator-valued equivalent of the frequency denominators that may cause divergence of the classical perturbation series. The results that are established here link the concept of quantum-mechanical integrability to a technical question, namely, the behavior of specific perturbation series.

Item Type: Article
Copyright, Publisher and Additional Information: © 1996 The American Physical Society. Reproduced in accordance with the publisher's self-archiving policy.
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: Repository Officer
Date Deposited: 23 Jun 2006
Last Modified: 14 Oct 2014 22:15
Published Version: http://dx.doi.org/10.1103/PhysRevA.53.2971
Status: Published
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1367

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