QMath9 gave a particular importance to summarize the state of the art of
the field in a perspective to transmit knowledge to younger scientists. The
main contributors to the field were gathered in order to communicate results,
open questions and motivate new research by the confrontation of different
view points. The edition of this book follows this spirit; the main effort of
the authors and editors is to help finding an access to the variety of themes
and the sometimes very sophisticated literature in Mathematical Physics.
The contributions of this book are organized in five topical groups: Quantum
Dynamics and Spectral Theory, Quantum Field Theory and Statistical
Mechanics, Quantum Kinetics and Bose-Einstein Condensation, Disordered
Systems and Random Operators, Semiclassical Analysis and Quantum Chaos.
This splitting is admittedly somewhat arbitrary, since there are overlaps between
the topics and the frontiers between the chosen groups may be quite
fuzzy. Moreover, there are close connections between the tools and techniques
used in the analysis of quite different physical phenomena. An introduction
to each theme is given. This plan is intended as a readers guide rather than
as an attempt to put contributions into well defined categories.