Let us consider the quantum/versus classical dynamics for Hamiltonians of the form \beq \label{ 0.1} H\_{ g}^{ \epsilon} := \frac{ P^2}{ 2}+ \epsilon \frac{ Q^2}{ 2}+ \frac{ g^2}{ Q^2} \edq where $\epsilon = \pm 1$, $g$ is a real constant. We shall in particular study the Quantum Fidelity between $H\_{ g}^{ \epsilon}$ and $H\_{ 0}^{ \epsilon}$ defined as \beq \label{ 0.2} F\_{ Q}^{ \epsilon}(t,g):= < \exp(-it H\_{ 0}^{ \epsilon})\psi, exp(-itH\_{ g}^ { \epsilon})\psi > \edq for some reference state $\psi$ 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.
Categories: math-ph math.MP