Gramespacher, Thomas and Weigert, S. (orcid.org/0000-0002-6647-3252) (1996) Small denominators, frequency operators, and Lie transforms for nearly integrable quantum spin systems. Physical Review A. pp. 2971-2982. ISSN 1094-1622
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.
|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:||22 Mar 2016 05:58|