The quantum fidelity for the time-dependent singular quantum oscillator

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dc.creatorCombescure, M.
dc.date2005-03-08
dc.date.accessioned2026-07-07T06:27:45Z
dc.date.available2026-07-07T06:27:45Z
dc.descriptionIn 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.
dc.identifierhttps://arxiv.org/abs/math-ph/0503013
dc.identifierhttp://arxiv.org/abs/math-ph/0503013
dc.identifierJournal of Mathematical Physics 47 (2006) 032102
dc.identifierdoi:10.1063/1.2178153
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97501
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleThe quantum fidelity for the time-dependent singular quantum oscillator
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