Classical and Quantum Chaos 2021/2022

Description

Chaos, popularly known as the butterfly effect, is a ubiquitous phenomenon that renders a system's evolution unpredictable due to extreme sensitivity to initial conditions. Within the context of classical physics, it often occurs in nonintegrable Hamiltonian systems and is characterized by positive Lyapunov exponents. On the other hand, the notion of nonintegrability and chaos in quantum physics is still not well-understood and is an area of active research. Several signatures have been studied in the literature to identify quantum chaos but all of them fall short in some way or the other. In this course, we will first discuss the notions of classical integrability, and classical chaos and its characterization with Lyapunov exponents. Then, we will discuss a few well-studied signatures of quantum chaos and the subtleties associated with them.