of quantum motion
The problem of the
stability of quantum motion has attracted a great interest, also in
relation to the field of quantum computation.
A quantity of central importance which has been on the focus of
many studies is the so-called fidelity
f(t), which measures the accuracy to which a quantum state can
be recovered by inverting, at time t, the dynamics with a perturbed
The analysis of this quantity has shown that, under appropriate
conditions, the decay of f(t) is exponential with a rate given by
the classical Lyapunov exponent (the Lyapunov exponent measures
the rate of exponential instability of classical motion).
correspondence in perturbed chaotic systems
We have discussed the behavior of fidelity for a classically
chaotic quantum system. We have shown the existence of a critical value
of the perturbation above which the quantum decay, exponential or
power-law, follows the classical one .
The independence of the decay rate
on the perturbation strength, discussed in the literature, is a
consequence of the quantum-classical correspondence of the relaxation
for the fidelity decay in the diffusive regime until the Heisenberg
 G. Benenti and G.
Casati, Quantum-classical correspondence in perturbed chaotic systems,
Phys. Rev. E 65, 066205 (2002).