Relaxation dynamics of isolated many-body quantum systems: Typical behavior for a preset initial value of an observable or in the presence of additional conserved quantities.

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We explore the quantum mechanical relaxation dynamics of systems with a large but finite number of degrees of freedom, which are prepared in a non-thermal initial state and which are strictly isolated from the rest of the world. Our first objective is to show that the overwhelming majority of initial states, featuring a common expectation value for any given observable, will also yield very similar expectation values for an arbitrary second observable at any later instant of time. Our second objective is to establish a universal quantitative prediction about typical relaxation properties of so-called integrable systems, exhibiting additional conserved quantities on top of the system energy.