Quantum chaos of a particle in a square well: Competing length scales and dynamical localization - art. no. 046210

The classical and quantum dynamics of a particle trapped in a one-dimension al infinite square well with a time-periodic pulsed field is investigated. This is a two-parameter non-KAM (Kolmogorov-Arnold-Moser) generalization of the kicked rotor, which can be seen as the standard map of particles subje cted to both smooth and hard potentials. The virtue of the generalization l ies in the introduction of an extra parameter R, which is the ratio of two length scales, namely, the well width and the field wavelength. If R is a n oninteger the dynamics is discontinuous and non-KAM. We have explored the r ole of R in controlling the localization properties of the eigenstates. In particular, the connection between classical diffusion and localization is found to generalize reasonably well. In unbounded chaotic systems such as t hese, while the nearest neighbor spacing distribution of the eigenvalues is less sensitive to the nature of the classical dynamics, the distribution o f participation ratios of the eigenstates proves to be a sensitive measure; in the chaotic regimes the latter is log-normal. We find that the tails of the well converged localized states are exponentially localized despite th e discontinuous dynamics while the bulk part shows fluctuations that tend t o be closer to random matrix theory predictions. Time evolving states show considerable R dependence, and tuning R to enhance classical diffusion can lead to significantly larger quantum diffusion for the same field strengths , an effect that is potentially observable in present day experiments.