Measurement-Induced Dynamical Quantum Thermalization

One of the fundamental problems of quantum statistical physics is, how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here we study by explicit time evolution for the generic model system of an interacting, trapped Bose gas with discrete single-particle levels, how the measurement of one or more observables subdivides the system into observed and non-observed Hilbert subspaces and the tracing over the non-measured quantum numbers defines an effective, thermodynamic bath, induces entanglement of the observed Hilbert subspace with the bath, and leads to bi-exponential approach of the entanglement entropy and of the measured observables to thermal equilibrium behavior as a function of time. We find this to be more generally fulfilled than in the scenario of the eigenstate thermalization hypothesis (ETH), namely for both local particle occupation numbers and non-local density correlation functions, and independent of the specific initial quantum state of the time evolution.