|
Descripción
|
|
|---|---|
| We look at the long-time behaviour of solutions to a semi-classical Schrödinger equation on the torus. We consider time scales which go to infinity when the semi-classical parameter goes to zero and we associate with each time-scale the set of semi-classical measures associated with all possible choices of initial data. On each classical invariant torus, the structure of semi-classical measures is described in terms of two-microlocal measures, obeying explicit propagation laws. We apply this construction in two directions. We first analyse the regularity of semiclassical measures, and we emphasize the existence of a threshold : for time-scales below this threshold, the set of semi-classical measures contains measures which are singular with respect to Lebesgue measure in the ?position? variable, while at (and beyond) the threshold, all the semi-classical measures are absolutely continuous in the ?position? variable, reflecting the dispersive properties of the equation. Second, the techniques of twomicrolocal analysis introduced in the paper are used to prove semiclassical observability estimates. The results apply as well to general quantum completely integrable systems. | |
|
Internacional
|
Si |
|
JCR del ISI
|
Si |
|
Título de la revista
|
American Journal of Mathematics |
|
ISSN
|
0002-9327 |
|
Factor de impacto JCR
|
1,35 |
|
Información de impacto
|
|
|
Volumen
|
|
|
DOI
|
|
|
Número de revista
|
|
|
Desde la página
|
1 |
|
Hasta la página
|
55 |
|
Mes
|
SIN MES |
|
Ranking
|
|