Lagrangian and Hamiltonian aspects of Josephson type media

Citation
Ak. Prykarpatsky et Ja. Zagrodzinski, Lagrangian and Hamiltonian aspects of Josephson type media, ANN IHP-PHY, 70(5), 1999, pp. 497-524
Citations number
21
Categorie Soggetti
Physics
Journal title
ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE
ISSN journal
02460211 → ACNP
Volume
70
Issue
5
Year of publication
1999
Pages
497 - 524
Database
ISI
SICI code
0246-0211(199905)70:5<497:LAHAOJ>2.0.ZU;2-5
Abstract
Dynamical properties of Josephson media are studied within Lagrangian and H amiltonian formalisms with gauge type constraints. A geometrical interpreta tion of the first class gauge type constraints involved is suggested basing on the Marsden-Weinstein momentum map reduction. An equivalent operatorial approach is also considered in detail giving rise to certain two essential ly different Poisson structures upon orbits of the Abelian gauge group, the first Poisson structure being nondegenerate in contrast to the second one- degenerated. The consideration of the Poisson structure associated with Jos ephson media are essentially augmented by means of introducing new Josephso n-Vlasov kinetic type equations endowed with the canonical Lie-Poisson brac ket. The reduction of the corresponding Hamiltonian flow explains the physi cal nature of the a priori involved constraints, (C) Elsevier, Paris.