Wave packet dynamics in an harmonic potential disturbed by disorder: Entropy, uncertainty, and vibrational revivals

We investigate the quantum and classical wave packet dynamics in an harmonic oscillator that is perturbed by a disorder potential. This perturbation causes the dispersion of a Gaussian wave packet, which is reflected in the coordinate-space and the momentum-space Shannon entropies, the latter being a measure for the amount of information available on a system. Regarding the sum of the two quantities, one arrives at an entropy that is related to the coordinate-momentum uncertainty. Whereas in the harmonic case, this entropy is strictly periodic and can be evaluated analytically, this behavior is lost if disorder is added. There, at selected times, the quantum mechanical probability density resembles that of a classical oscillator distribution function, and the entropy assumes larger values. However, at later times and dependent on the degree of disorder and the chosen initial conditions, quantum mechanical revivals occur. Then, the observed effects are reversed, and the entropy may decrease close to its initial value. This effect cannot be found classically.