Unitarity and irreversibility in chaotic systems

Journal Article · Tue Dec 15 04:00:00 EST 1992 · Physical Review A. General Physics; (United States)

DOI:https://doi.org/10.1103/PhysRevA.46.7401· OSTI ID:6937373

Hasegawa, H H; Saphir, W C ^[1]

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1. Center for Studies in Statistical Mechanics and Complex Systems, University of Texas at Austin, Austin, Texas 78712 (United States) International Solvay Institutes for Physics and Chemistry, 1050 Brussels (Belgium)

We analyze the spectral properties of the Perron-Frobenius operator [ital U], associated with some simple highly chaotic maps. We obtain a spectral decomposition of [ital U] in terms of generalized eigenfunctions of [ital U] and its adjoint. The corresponding eigenvalues are related to the decay rates of correlation functions and have magnitude less than one, so that physically measurable quantities manifestly approach equilibrium. To obtain decaying eigenstates of unitary and isometric operators it is necessary to extend the Hilbert-space formulation of dynamical systems. We describe and illustrate a method to obtain the decomposition explicitly.

• DOE Contract Number: FG05-88ER13897
• OSTI ID: 6937373
• Journal Information: Physical Review A. General Physics; (United States), Journal Name: Physical Review A. General Physics; (United States) Vol. 46:12; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BANACH SPACE
CORRELATION FUNCTIONS
EIGENFUNCTIONS
EIGENVALUES
FUNCTIONS
HILBERT SPACE
IRREVERSIBLE PROCESSES
MAPS
MATHEMATICAL SPACE
MECHANICS
SPACE
STATISTICAL MECHANICS
UNITARITY