1 research outputs found
Quantum and Classical Fidelity for Singular Perturbations of the Inverted and Harmonic Oscillator
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 , is a real
constant. We shall in particular study the Quantum Fidelity between
and 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 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 is
varied.Comment: To be published in Journal of Mathematical Analysis and Application