Typicality of observables and states

Abstract

The implementation of the typicality approach to quantum systems as introduced in Chaps. 6 and 7 is further elaborated on. Thus, a concrete class of accessible regions as formally introduced in sect. 6 is given. To start with, expectation values of observables are investigated for typicality. We essentially find that typicality can be expected for observables which are defined on high-dimensional Hilbert spaces, but feature bound spectra within the accessible state space. The typical values of the observable are in accord with Boltzmann's principle of "equal a priori probabilities." Furthermore, typicality of a state rather than for an observable is introduced. We find that, while there may very well be such typicality of some observables there is no typicality of states for non-composite systems. This points toward the investigation of composite systems. © 2009 Springer-Verlag Berlin Heidelberg.