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q-deformations of statistical mechanical systems and motives over finite fields (1704.06367v1)
Published 21 Apr 2017 in math-ph and math.MP
Abstract: We consider q-deformations of Witt rings, based on geometric operations on zeta functions of motives over finite fields, and we use these deformations to construct q-analogs of the Bost-Connes quantum statistical mechanical system. We show that the q-deformations obtained in this way can be related to Habiro ring constructions of analytic functions over the field with one element and to categorifications of Bost-Connes systems.