HAL : in2p3-00023855, version 1
 arXiv : math-ph/0503013
 DOI : 10.1063/1.2178153
 Journal of Mathematical Physics 47 (2006) 032102
 The quantum fidelity for the time-dependent singular quantum oscillator
 (2006)
 In this paper we perform an exact study of Quantum Fidelity'' (also called Loschmidt Echo) for the time-periodic quantum Harmonic Oscillator of Hamiltonian : $\hat H_{g}(t):=\frac{P^2}{2 }+ f(t)\frac{Q^2}{2}+\frac{g^2}{Q^2}$ when compared with the quantum evolution induced by $\hat H_{0}(t)$ ($g=0$), in the case where $f$ is a $T$-periodic function and $g$ a real constant. The reference (initial) state is taken to be an arbitrary generalized coherent state'' in the sense of Perelomov. We show that, starting with a quadratic decrease in time in the neighborhood of $t=0$, this quantum fidelity may recur to its initial value 1 at an infinite sequence of times {$t_{k}$}. We discuss the result when the classical motion induced by Hamiltonian $\hat H_{0}(t)$ is assumed to be stable versus unstable. A beautiful relationship between the quantum and the classical fidelity is also demonstrated.
 Thème(s) : Physique/Physique mathématiquePhysique/Physique Quantique
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 in2p3-00023855, version 1 http://hal.in2p3.fr/in2p3-00023855 oai:hal.in2p3.fr:in2p3-00023855 Contributeur : Sylvie Florès <> Soumis le : Mardi 8 Mars 2005, 10:23:43 Dernière modification le : Mercredi 19 Avril 2006, 11:42:45