Observational-entropic study of Anderson localization

The notion of the thermodynamic entropy in context quantum mechanics is a controversial topic. Although there were proposals to refer von Neumann as entropy, it has its own limitations. observational been developed generalization Boltzmann and presently one most promising candidates provide clear well-defined understanding mechanics. In this paper, we study behavior localization-delocalization transition for one-dimensional Aubrey-Andr\'e (AA) model. We find that typical midspectrum states, delocalized phase observation grows rapidly with coarse-grain size saturates maximal value, whereas localized growth logarithmic. Moreover, given coarse-graining, increases logarithmically system phase, obeys area law phase. also increase followed by quench logarithmic time well at point, oscillates. Finally, venture self-dual property AA model using momentum space coarse graining.