Publicação
Focal decomposition, renormalization and semiclassical physics
| Resumo: | 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. |
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| Autores principais: | C. A. A. de Carvalho |
| Outros Autores: | M. M. Peixoto; D. Pinheiro; A. A. Pinto |
| Assunto: | Matemática Mathematics |
| Ano: | 2011 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade do Porto |
| Idioma: | inglês |
| Origem: | Repositório Aberto da Universidade do Porto |
| Resumo: | 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. |
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