Condensed Matter Seminar: Tianci Zhou, University of Illinois at Urbana-Champaign - “The development of quantum chaos”

Chaos is characterized by its fast scrambling and extreme complexity. In this talk, we will first inspect the chaotic unitary evolution operator and see how its contents and complexity grow with time. In the complementary state point of view, we motivate the notion of distance between the wave functions. By tuning the interactions, we find an exponentially growing distance of two initially “nearby” states. We relate this distance to the out-of-time-ordered correlator, and thus identify the growth rate as the quantum Lyapunov exponent.