CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS
UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR
KREKOVA 2 SI-2000 MARIBOR SLOVENIA
Phone +(386) (2) 2355 350 and 2355 351 $\bullet$ Fax +(386) (2) 2355 360
Robnik@uni-mb.si $\bullet$ www.camtp.uni-mb.si
PROF.DR. MARKO ROBNIK, DIRECTOR

Seminarsko predavanje
Centra za uporabno matematiko in teoreticno fiziko

Quantum freeze of fidelity decay for a class of integrable dynamics

Doc.Dr. Tomaz Prosen
Oddelek za fiziko, Fakulteta za matematiko in fiziko
Univerza v Ljubljani

Abstract: We discuss quantum fidelity decay of classically regular dynamics, in particular for an important special case of a vanishing time averaged perturbation operator. A complete semiclassical picture of this situation is derived in which we show that the quantum fidelity of individual coherent initial states exhibits three different regimes in time: (i) first it follows the corresponding classical fidelity up to time $t_1 \sim \hbar^{-1/2}$, (ii) then it freezes on a plateau of constant value, (iii) and after a time scale $t_2 \sim \min\{\hbar^{1/2}\delta^{-2},\hbar^{-1/2}\delta^{-1}\}$ it exhibits fast ballistic decay as $\exp(-{\rm const}\,\delta^4 t^2/\hbar)$ where $\delta$ is a strength of perturbation. A similar picture is worked out also for general initial states, and specifically for random initial states, where $t_1 \sim 1$, and $t_2 \sim \delta^{-1}$. This prolonged stability of quantum dynamics in the case of a vanishing time averaged perturbation could prove to be useful in designing quantum devices.

Seminarsko predavanje bo v petek, 5. septembra 2003 ob 17:15 uri v seminarski sobi CAMTP na Krekovi 2, pritlicje desno. Vljudno vabljeni vsi zainteresirani, tudi študentje.

Prof.Dr. Marko Robnik
-- Direktor CAMTP --