Many-body chaos and dynamical transitions: Classical to quantum and back again

Chaos is an important characterization of classical dynamical systems. However, in recent years, a quantum Lyapunov exponent λL, and a butterfly velocity vB for ballistic spread of local perturbation, computed from the so-called out-of-time-order commutator (OTOC) have emerged as important measures for chaos and thermalization in interacting quantum many-body systems having some well-defined semiclassical limit. In the first part of the talk, I will describe curious interplay of chaos, quantum fluctuations, symmetry breaking and complex dynamics across dynamical transition in a quantum spin glass model. I will discuss the implications of the results in the classical limit of the model which describes dynamics in supercooled liquid in structural glasses. In the second part of the talk, I will talk about a surprising noise-induced many-body chaotic to non-chaotic transition in the classical Langevin dynamics of interacting integrable and non-integrable systems.

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