Excitation of Small Quantum Systems by High-Frequency Fields

Semiclassical quantization of separatrix maps

Quantization of energy balance equations, which describe a separatrixlike motion is presented. The method is based on an exact canonical transformation of the energy-time pair to the action-angle canonical pair, (E,t)-->(I,theta). Quantum mechanical dynamics can be studied in the framework of the new Hamiltonian. This transformation also establishes a relation between a wide class of the energy balance equations and dynamical localization of classical diffusion by quantum interference, that was studied in the field of quantum chaos. An exact solution for a simple system is presented as well.

Quantum recurrences: probe to study quantum chaos

We study the phase space of periodically modulated gravitational cavity by means of quantum recurrence phenomena. We report that the quantum recurrences serve as a tool to connect phase space of the driven system with a spectrum in the quantum domain. With the help of quantum recurrences we investigate the quasienergy spectrum of the system for a certain fixed modulation strength. In addition, we study transition of spectrum from discrete to continuum as a function of modulation strength.

Quantum response for chaotic resonances

Chaotic dynamics of conducting electrons in the presence of a high-frequency electromagnetic field and a constant homogeneous magnetic field is considered. It is shown that quantum fluctuations become important in this case on a time scale shorter than mean free time. Nonperturbative approach for calculation of a kinetic coefficient (conductivity) is developed. An analytical expression for the kinetic coefficient as a function of the magnetic field and a localization length is obtained. Dependence of the conductivity on the quantum localization length is studied.