The geometric phase in nonlinear dissipative systems

Journal Article · Fri Oct 30 00:00:00 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), Vol. 6:25; ISSN 0217-9849
• Country of Publication: United States
• Language: English

Related Subjects

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