Dynamical Equilibration of Quantum Systems

Equilibration is the process by which evolving properties of a system approach a steady state. Equilibration occurs in nature at diverse scales, from cosmological to quantum. This talk will focus on how quantum systems approach equilibrium. I will review conditions under which isolated quantum systems equilibrate. These conditions are rather general and intuitive: if a system's initial state populates enough distinct energy gaps, any observable eventually reaches an equilibrium and remains close to it. However, characterizing the timescales over which such equilibration happens is a trickier problem.The equilibration timescales of different observables in a given system can differ exponentially in the size of the system. I will present general results that allow discriminating observables' equilibration timescales and conclude by discussing some of the many open problems in the field.