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We present an extreme localization mechanism induced by a magnetic field for tight-binding electrons in two-dimensional structures. This original phenomenon is investigated for a large class of tilings (periodic, quasiperiodic, or random). We are led to introduce Aharonov-Bohm cages that are defined as the set of sites eventually visited by a wave packet that can, for particular values of the magnetic flux, be bounded. We finally discuss the quantum dynamics which exhibit an uncommon pulsating behavior.
Vidal et al. (1998) studied this question.