SEMINAIRE MERCREDI 17 DECEMBRE 2003
13 heures 45
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Roman Schubert
Université de Bristol

Title: Expectation values for large time evolution of lagrangean states.

Summary: We study the behaviour of quantum mechanical expectation values in
Lagrangian states in the limit \hbar -> 0 and t -> \infty. We show
that it depends strongly on the dynamical properties of the
corresponding classical system. If the classical system is strongly
chaotic, i.e., Anosov, then the expectation values tend to a universal
limit. This can be viewed as an analog of mixing in the classical
system. If the classical system is integrable, then the expectation
values need not converge, and if they converge their limit depends on
the initial state. An additional difference occurs in the timescales
for which we can prove this behaviour, in the chaotic case we get only
up to Ehrenfest time, t is nearly \ln(1/\hbar), whereas for integrable
system we have much larger time range.