I will discuss out-of-equilibrium dynamics in chaotic quantum many-body systems, emphasising that some basic dynamical questions about correlations and entanglement can be reduced to effective classical stat mech problems (involving random walks, domain walls, percolation, traveling waves, etc.).
Quantum many-body dynamics far from the ground state: the search for universality. (Quantum chaos and complexity; entanglement entropy; decoherence and the emergence of hydrodynamics.) Many-body dynamics in the NISQ era. Random quantum circuits as simple models.
Lieb-Robinson and causality. Correlations in quantum circuits: mapping to a classical Markov process. Two-point functions and spacetime trajectories. “Unbinding” phase transition for spacetime trajectories. Questions about efficient simulation of quantum systems.
Entanglement entropy as free energy of a membrane in an effective classical model. Coarse-grained evolution equation for the entanglement entropy.
Motivations: quantum trajectories of continually measured systems. Entanglement transitions: schematic picture. Replica picture (overview)
The simplest example of an entanglement phase transition and reduction to a recursion relation on a tree.