Random matrix theory; Quantum chaos;

How isolated quantum systems approach and reach equilibrium and thermalization constitutes a long-standing question, which goes back to the very early days of quantum mechanics. Unitary time evolution indeed seems to put severe limitations on the possibility for a closed quantum system to reach thermal equilibrium. This tension is usually solved by means of the celebrated Eigenstate Thermalization Hypothesis (ETH) which ultimately allows for local observables to thermalize their expectation values. The intuition behind ETH strongly relies on random matrix theory.