Lecture

Quantum Chaos and Scrambling

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Description

This lecture delves into the concept of scrambling in quantum chaotic systems, where small perturbations can lead to large effects over time. The discussion connects classical chaos to quantum chaos, emphasizing sensitivity to initial conditions. The instructor explores the quantum mechanical counterpart of this phenomenon, known as scrambling, and its implications in spectral statistics. The lecture also touches upon the implications of chaos in black holes and the behavior of out-of-time-ordered correlators. Various concepts such as Lyapunov exponents, conformal field theory, and the bound on chaos are discussed, shedding light on the intricate interplay between chaos and quantum mechanics.

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In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter. Mathematically, finding an exact solution means finding a Lorentzian manifold equipped with tensor fields modeling states of ordinary matter, such as a fluid, or classical non-gravitational fields such as the electromagnetic field.

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