The geometric phase in nonlinear dissipative systems

Journal Article · Fri Oct 30 04:00:00 EST 1992 · Modern Physics Letters B; (Singapore)

DOI:https://doi.org/10.1142/S0217984992001265· OSTI ID:7018431

Ning, C Z; Haken, H ^[1]

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1. Inst. fur Theoretische Physik und Synergetik, Univ. Stuttgart, Pfaffenwalding 57/IV, D-7000 Stuttgart 80 (Germany)

In this paper, the authors review the recent progress made in generalizing the concept of the geometric phase to nonlinear dissipative systems. The authors first illustrate the usual form of the parallel transport law with an elementary example of the parallel shift of a line on the complex plane. Important results about the non-adiabatical geometric (Aharonov and Anandan or AA) phase [sup 18] for the Schrodinger equations are reviewed in order to make a comparison with results for dissipative systems. The authors show that a geometric phase can be defined for dissipative systems with the cyclic attractors. Systems undergoing the Hopf bifurcation with a continuous symmetry are shown to possess such cyclic attractors. Examples from laser physics are discussed to exhibit the applicability of our formalism and the widespread existence of the geometric phase in dissipative systems.

• OSTI ID: 7018431
• Journal Information: Modern Physics Letters B; (Singapore), Journal Name: Modern Physics Letters B; (Singapore) Vol. 6:25; ISSN 0217-9849; ISSN MPLBET
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
426002 -- Engineering-- Lasers & Masers-- (1990-)
661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AHARONOV-BOHM EFFECT
ATTRACTORS
DIFFERENTIAL EQUATIONS
DOCUMENT TYPES
ENERGY LOSSES
EQUATIONS
GEOMETRY
LASERS
LOSSES
MATHEMATICS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SHIFT
REVIEWS
SCHROEDINGER EQUATION
USES
WAVE EQUATIONS