Universal Hitting Time Statistics for Integrable Flows.

The perceived randomness in the time evolution of "chaotic" dynamical systems can be characterized by universal probabilistic limit laws, which do not depend on the fine features of the individual system. One important example is the Poisson law for the times at which a particle with random initial data hits a small set. This was proved in various settings for dynamical systems with strong mixing properties.

Generation of ultrahigh and tunable repetition rates in CW injection-seeded frequency-shifted feedback lasers.

We show both theoretically and experimentally that frequency-shifted feedback (FSF) lasers seeded with a single frequency laser can generate Fourier transform-limited pulses with a repetition rate tunable and limited by the spectral bandwidth of the laser. We demonstrate experimentally in a FSF laser with a 150 GHz spectral bandwidth, the generation of 6 ps-duration pulses at repetition rates tunable over more than two orders of magnitude between 0.24 and 37 GHz, by steps of 80 MHz.

Nodal domain statistics for quantum maps, percolation, and stochastic Loewner evolution.

We develop a percolation model for nodal domains in the eigenvectors of quantum chaotic torus maps. Our model follows directly from the assumption that the quantum maps are described by random matrix theory. Its accuracy in predicting statistical properties of the nodal domains is demonstrated for perturbed cat maps and supports the use of percolation theory to describe the wave functions of general Hamiltonian systems.

Random matrices and quantum chaos.

The theory of random matrices has far-reaching applications in many different areas of mathematics and physics. In this note, we briefly describe the state of the theory and two of the perhaps most surprising appearances of random matrices, namely in the theory of quantum chaos and in the theory of prime numbers.