The future directions of research are the following:
To continue investigations of microwave ionization of chaotic Rydberg atoms in more close contact with experimental groups of Beterov, Gallagher and Walther in the frame of the EC net grant "Quantum transport on an atomic scale". Investigation of quantum Poincaré recurrences in the systems with divided phase space with appilations to Rydberg and cold atoms, first results are presented in [108] (with G.Benenti, G.Casati and G.Maspero).
To study the eigenstate properties of 3-dimensional rough billiards (rough sphere) with K.Frahm.
Investigation of quantum spin glass models in finite dimensions, studies of quantum chaos regime in finite spin glass systems.
To develop the new direction of research related to the emergence of quantum chaos in quantum computers due to interqubit interaction.
The main direction of future research is planed to be related with the problems of interaction, disorder, Anderson localization and transport. The results of section 3.7 should be used to understand the reasons of metal-insulator transition in 2-dimensional disordered systems observed in experiments of Kravchenko et al.. Since the experiment indicates importance of spin effects the investigations of disordered spin models can also represent some interest (with A.Barelli, K.Frahm and B.Georgeot). This direction of research forms the basis for theses of Gaetan Caldara and José Lages started this year in the group of quantum chaos. To study effects of disorder on superconductivity, first results in this direction are presented in [109].