Quantum chaos

The group studies quantum chaos: how the irregular, unpredictable motion of classically chaotic systems leaves its signature in the discrete energy spectra and wavefunctions of their quantum counterparts. A central theme is universality, the observation that the statistics of energy levels in chaotic systems follow the predictions of random matrix theory, independent of microscopic detail. The work seeks to derive these statistical laws from first principles, connecting periodic orbits and classical dynamics to spectral correlations through semiclassical methods.

A distinctive thread is the use of quantum graphs, networks of one-dimensional bonds whose wave equations reproduce the spectral statistics of chaotic systems while remaining mathematically tractable. These models serve as a controlled laboratory for testing conjectures about universality, and they connect spectral physics to combinatorics, number theory, and the inverse problem of recovering a system's geometry from its spectrum. The group also studies nodal structures, the patterns of zeros and sign domains of eigenfunctions, which carry their own statistical information about the underlying dynamics and offer a complementary window onto the classical-to-quantum correspondence.