Stability
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
Hamiltonian.
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).
Quantum-classical
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 [1].
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
process.
Quantum-classical correspondence
for the fidelity decay in the diffusive regime until the Heisenberg
time scale.
References
[1] G. Benenti and G.
Casati, Quantum-classical correspondence in perturbed chaotic systems,
Phys. Rev. E 65, 066205 (2002).
