14:00
On the density of complex eigenvalues of sub-unitary scattering matrices in quantum chaotic systems.
Abstract
The scattering matrix in quantum mechanics must be unitary to ensure the conservation of the number of particles, hence their
eigenvalues are unimodular. In systems with fully developed Quantum Chaos the statistics of those unimodular
eigenvalues is well described by the Poisson kernel.
However, in real experiments the associated scattering matrix is sub-unitary due to intrinsic losses, and
the moduli of S-matrix eigenvalues become non-trivial, yet the corresponding theory is not well-developed in general.
I will present some results for the mean density of those moduli in the framework of random matrix models for the case of broken time-reversal invariance,
and discuss a way to get a generalization of the Poisson kernel to systems with uniform losses.