Statistical properties of the localization measure of chaotic eigenstates and the spectral statistics in a mixed-type billiard.

We study the quantum localization in the chaotic eigenstates of a billiard with mixed-type phase space [J. Phys. A: Math.

Fermi acceleration in chaotic shape-preserving billiards.

We study theoretically and numerically the velocity dynamics of fully chaotic time-dependent shape-preserving billiards. The average velocity of an ensemble of initial conditions generally asymptotically follows the power law 〈v〉 = n(β) with respect to the number of collisions n. If a shape of a fully chaotic time-dependent billiard is not preserved it is well known that the acceleration exponent is β = 1/2.

Exponential Fermi acceleration in general time-dependent billiards.

We show, that under very general conditions, a generic time-dependent billiard, for which a phase space of corresponding static (frozen) billiards is of the mixed type, exhibits the exponential Fermi acceleration in the adiabatic limit. The velocity dynamics in the adiabatic regime is represented as an integral over a path through the abstract space of invariant components of corresponding static billiards, where the paths are generated probabilistically in terms of transition-probability matrices. We study the statistical properties of possible paths and deduce the conditions for the exponential Fermi acceleration.

Statistical properties of one-dimensional parametrically kicked Hamilton systems.

We study the one-dimensional Hamiltonian systems and their statistical behavior, assuming the initial microcanonical distribution and describing its change under a parametric kick, which by definition means a discontinuous jump of a control parameter of the system. Following a previous work by Papamikos and Robnik [J. Phys.

Quantum localization of chaotic eigenstates and the level spacing distribution.

The phenomenon of quantum localization in classically chaotic eigenstates is one of the main issues in quantum chaos (or wave chaos), and thus plays an important role in general quantum mechanics or even in general wave mechanics. In this work we propose two different localization measures characterizing the degree of quantum localization, and study their relation to another fundamental aspect of quantum chaos, namely the (energy) spectral statistics. Our approach and method is quite general, and we apply it to billiard systems.