Quantum Chaos: Routes to RMT Statistics and Beyond (08w5091)

Objectives

The main objective of the conference is to bring together
physicists and mathematicians working on spectral statistics and transport
properties of the quantum chaotic systems. As partly explained in the
overview of the research area, the community is fractured along various lines.
Firstly, there is a mathematicians-physicists divide. Right now the area is
at an important point when physicists are feeling that a significant progress
has been made towards proving the RMT conjecture while mathematicians largerly
feel that the results are not rigorous enough to be of interest. However,
often in the past the rigorous mathematical research was fueled by
``physical'' intuition, while mathematical criticism can give physicists a
better view of limitations of the current methods (and a glimpse of what lies
beyond). Thus it is very important that two communities talk to each other.

On the other hand, there is a divide where some people are using periodic orbit
expansions (trace formulae) while others use supersymmetric field theory. Yet
we feel that cross-understanding of these two methods is absolutely crucial
for future progress. In particular, it may help to make the result obtained
by the two methods more mathematically acceptable.

Using quantum graphs as a toy model is especially relevant to the aims of the
conference. This is primarily because both approaches become significantly
simpler when considered on graphs. Recent applications to the question of RMT
statistics on graphs of super-symmetry methods and of periodic-orbit
expansions have already led to better understanding of both advantages and
disadvantages of these methods. In addition, certain classes of graphs (star
graphs and trees) have become the rare examples of systems where the spectral
statistics can be derived rigorously.

Other conferences in the field:
We feel this conference is unique. There has not been a conference aimed at uniting these complementary but distinct communities since the late 90's. It is certainly time to strengthen interactions between these communities again.

http://www.math.tamu.edu/~berko/banff/