Special Probability Seminar: A random matrix model towards the quantum chaos transition conjecture

The Quantum Chaos Conjecture has long fascinated researchers, postulating a critical spectrum phase transition that separates integrable systems from chaotic systems in quantum mechanics. In the real of integrable systems, eigenvectors remain localized, and local eigenvalue statistics follow the Poisson distribution. Conversely, chaotic systems exhibit delocalized eigenvectors, with local eigenvalue statistics mirroring the Sine kernel distribution, akin to the standard random matrix ensembles GOE/GUE.

This talk delves into the heart of the Quantum Chaos Conjecture, presenting a novel approach through the lens of random matrix models. By utilizing these models, we aim to provide a clear and intuitive demonstration of the same phenomenon, shedding light on the intricacies of this long-standing conjecture.