Focal decomposition, renormalization and semiclassical physics

• Type: Article in International Scientific Journal
• Date: 2011

Authors

C. A. A. de Carvalho (Author) Other; M. M. Peixoto (Author) Other; D. Pinheiro (Author) Other; A. A. Pinto (Author) FCUP

Journal

Title: Journal of Difference Equations and Applications

Vol. 17 No. 7

Pages: 1019-1029

ISSN: 1023-6198

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 3 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-002-X3S

DOI: 10.1080/10236191003685916

Abstract (EN): We review some recent results concerning a connection between focal decomposition, renormalization and semiclassical physics. The dynamical behaviour of a family of mechanical systems which includes the pendulum at small neighbourhoods of the equilibrium but after long intervals of time can be characterized through a renormalization scheme acting on the dynamics of this family. We have proved that the asymptotic limit of this renormalization scheme is universal: it is the same for all the elements in the considered class of mechanical systems. As a consequence, we have obtained an asymptotic universal focal decomposition for this family of mechanical systems which can now be used to compute estimates for propagators in semiclassical physics.

Language: English

Type (Professor's evaluation): Scientific

Notes: We review some recent results concerning a connection between focal decomposition, renormalization and semiclassical physics. The dynamical behaviour of a family of mechanical systems which includes the pendulum at small neighbourhoods of the equilibrium but after long intervals of time can be characterized through a renormalization scheme acting on the dynamics of this family. We have proved that the asymptotic limit of this renormalization scheme is universal: it is the same for all the elements in the considered class of mechanical systems. As a consequence, we have obtained an asymptotic universal focal decomposition for this family of mechanical systems which can now be used to compute estimates for propagators in semiclassical physics.

No. of pages: 11