Poincaré's theorem and subdynamics for driven systems

Lee Jing-Yee and S. Tasaki

Physica A: Statistical Mechanics and its Applications, 1992, vol. 182, issue 1, 59-99

Abstract: 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.

Date: 1992
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/037843719290230N
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:182:y:1992:i:1:p:59-99

DOI: 10.1016/0378-4371(92)90230-N

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().