• Citer

Poincaré's theorem and subdynamics for driven systems

par Jing-Yee, Lee;Tasaki, Shuichi
Référence Physica. A, 182, 1-2, page (59-99)
Publication Publié, 1992-03

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

Large dynamical systems with explicit time dependence will be studied. For these systems (which we call driven systems), there exist resonances between internal frequencies and/or between internal and external frequencies. As in the time-independent case, the usual canonical or unitary perturbation theory leads to divergences due to the resonances. As a result, there exist no trajectories analytic in both the coupling constant and the initial data. This is a generalization of Poincaré's theorem on non-integrability and extends the notion of large Poincaré systems (LPS), i.e., systems with a continuous spectrum and a continuous set of resonances. Here the resonances involve external frequencies. Along the line of the subdynamics theory developed by Prigogine and his co-workers, we study LPS within the Liouville-space formalism. We construct projection operators which decompose the equations of motion and are analytic in the coupling constant. Our approach recovers Coveney's theory of time-dependent subdynamics but is based on recursion formulas, which significantly simplify the construction of the projection operators. These projectors are non-Hermitian and provide a description with broken time symmetry. As an application, we study the modification of the well-known three stages of the decay process from a time-dependent perturbation. © 1992.