Lecturer: Dr. Vladimir Al. Osipov
Affiliation: Faculty of Physics,Universität Duisburg-Essen
Abstract:
The eigenvalues of integrable systems can be
explicitly related to the set of integer numbers by
the Bohr-Sommerfeld quantisation rules, while
no such regular structure exists for systems with
complex dynamics. The famous Wigner-Dyson-
Mehta conjecture asserts that the spectrum of
complex quantum systems on the scales of the
mean level spacing between eigenvalues is
universal and can be described by Random
Matrix Ensembles. Such spectral statistics have
been observed in many real and numerical
experiments for systems ranging from
compound nuclei to complex molecules and
atoms. So far, however, the scope of theoretical
approaches was mainly focused on systems of a
few particles with low-dimensional phase spaces.
The principal theoretical result was the
formulation of the semiclassical theory of
periodic orbits by Sieber and Richter. They
showed that the universal properties of quantum
systems with classically chaotic dynamics can be
accounted for through correlations between
partner periodic orbits with small action
differences.
In our work we consider N-particle chaotic
systems with local homogeneous interactions,
where N is not necessarily small. Based on a
model of coupled cat maps we demonstrate
emergence of a new mechanism for correlation
between periodic orbit actions. In particular, we
show the existence of partner orbits which are
specific to many-particle systems only. Moreover,
they become dominant for sufficiently large N
and seem to be necessary for construction of a
consistent many-particle semiclassical theory.