Chaos and Thermalization in Quantum Many-Body Systems and Gravity

Abstract

In this thesis, we explore the process of thermalization in chaotic quantum many-body systems with the help of concepts and techniques from quantum information theory. We identify a universal dynamical process in the Heisenberg evolution of operators known as void formation, and use it to provide a new characterization of information spreading in chaotic systems. We also develop a technique called the equilibrium approximation, which allows us to express information-theoretic quantities in pure states evolved to late times in chaotic quantum many-body systems purely in terms of equilibrium quantities, and to do so in a way that is consistent with unitarity. This technique allows us to calculate correlation measures such as entanglement entropy or logarithmic negativity, as well as measures of information recovery from subsystems, in chaotic systems ranging from spin chains and quantum field theories to black holes. For evaporating black holes, the equilibrium approximation for entanglement entropy provides a systematic derivation of certain recent prescriptions for addressing Hawking’s information loss paradox, and explains their physical origin. The equilibrium approximation for logarithmic negativity and Petz map fidelity leads to surprising new predictions for entanglement structure and information transfer between a black hole and its radiation.