Iomin A, Fishman S, Zaslavsky GM. Semiclassical quantization of separatrix maps.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003;
67:046210. [PMID:
12786463 DOI:
10.1103/physreve.67.046210]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2002] [Indexed: 05/24/2023]
Abstract
Quantization of energy balance equations, which describe a separatrixlike motion is presented. The method is based on an exact canonical transformation of the energy-time pair to the action-angle canonical pair, (E,t)-->(I,theta). Quantum mechanical dynamics can be studied in the framework of the new Hamiltonian. This transformation also establishes a relation between a wide class of the energy balance equations and dynamical localization of classical diffusion by quantum interference, that was studied in the field of quantum chaos. An exact solution for a simple system is presented as well.
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