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Optimal decay of Wannier functions in Chern and quantum Hall insulators. (English) Zbl 1400.82249
The paper aims to contribute to the understanding of some transport properties of quantum systems out of equilibrium. For instance, it tries to explain the conductivity properties of solids, starting from some basic properties. To this end, one analyzes the rate of the decay of composite of the Wannier functions associate to the grapped periodic Hamiltonian of the system. The results, which deal with a kind of localization dichotomy, are stated in terms of families of projectors which characterize crystals. Loosely speaking, the mathematics of the paper turns around composite Wannier functions.

82C70 Transport processes in time-dependent statistical mechanics
81V70 Many-body theory; quantum Hall effect
82D10 Statistical mechanical studies of plasmas
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