Classical statistical mechanics of a few-body interacting spin model

We study the emergence of Boltzmann's law for the "single-particle energy distribution" in a closed system of interacting classical spins. It is shown that for a large number of particles Boltzmann's law may occur, even if the interaction is very strong. Specific attention is paid to classical analogs of the average shape of quantum eigenstates and "local density of states," which are very important in quantum chaology. Analytical predictions are then compared with numerical data.

Anderson localization as a parametric instability of the linear kicked oscillator

We rigorously analyze the correspondence between the one-dimensional standard Anderson model and a related classical system, the "kicked oscillator" with noisy frequency. We show that the Anderson localization corresponds to a parametric instability of the oscillator, the localization length being related to the rate of exponential growth of the energy of the oscillator. Analytical expression for a weak disorder is obtained, which is valid both inside the energy band and at the band edge.

Wave packet dynamics in energy space, random matrix theory, and the quantum-classical correspondence

We apply random-matrix-theory (RMT) to the analysis of evolution of wave packets in energy space. We study the crossover from ballistic behavior to saturation, the possibility of having an intermediate diffusive behavior, and the feasibility of strong localization effect. Both theoretical considerations and numerical results are presented. Using quantal-classical correspondence considerations we question the validity of the emerging dynamical picture. In particular, we claim that the appearance of the intermediate diffusive behavior is possibly an artifact of the RMT strategy.