Semiclassical structure of chaotic resonance eigenfunctions

• Autor(a) principal: Keating, Jonathan Philipe
• Data de Publicação: 2006
• Outros Autores: Novaes, Marcel, Prado, Sandra Denise, Sieber, M.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFRGS
• Texto Completo: http://hdl.handle.net/10183/99395
• topic: Caos; Autovalores e autofunções; Teoria quântica; Sistemas caóticos

We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the nonunitary quantum propagator and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as @ ! 0 on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates {Ψ(h)} h→0 is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker’s map, for which the probability density in position space is observed to have self-similarity properties.