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.


[1]  G. Benenti and G. Casati, Quantum-classical correspondence in perturbed chaotic systems, Phys. Rev. E 65, 066205 (2002).