Quantum and Classical Fidelity for Singular Perturbations of the Inverted and Harmonic Oscillator

Simple item page
dc.creatorCombescure, M.
dc.creatorCombescure, A.
dc.date2006-03-15
dc.date.accessioned2026-07-07T07:06:21Z
dc.date.available2026-07-07T07:06:21Z
dc.descriptionLet us consider the quantum/versus classical dynamics for Hamiltonians of the form \beq \label{0.1} H\_{g}^ε := \frac{P^2}{2}+ ε\frac{Q^2}{2}+ \frac{g^2}{Q^2} \edq where $ε= \pm 1$, $g$ is a real constant. We shall in particular study the Quantum Fidelity between $H\_{g}^ε$ and $H\_{0}^ε$ defined as \beq \label{0.2} F\_{Q}^ε(t,g):= < \exp(-it H\_{0}^ε)ψ, exp(-itH\_{g}^ ε)ψ> \edq for some reference state $ψ$ in the domain of the relevant operators. We shall also propose a definition of the Classical Fidelity, already present in the literature (\cite{becave1}, \cite{becave2}, \cite{ec}, \cite{prozni}, \cite{vepro}) and compare it with the behaviour of the Quantum Fidelity, as time evolves, and as the coupling constant $g$ is varied.
dc.descriptionTo be published in Journal of Mathematical Analysis and Applications
dc.identifierhttps://arxiv.org/abs/math-ph/0603041
dc.identifierhttp://arxiv.org/abs/math-ph/0603041
dc.identifierJournal of Mathematical Analysis and Applications 326 (2006) 908-928
dc.identifierdoi:10.1016/j.jmaa.2006.03.044
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109990
dc.subjectMathematical Physics
dc.titleQuantum and Classical Fidelity for Singular Perturbations of the Inverted and Harmonic Oscillator
dc.typetext

Files

Collections

arXiv