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8 pages, 6 figuresThis papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a simple framework leading to fully-analytical developments. Particular attention is devoted to the case of a time-dependent potential, which results in a rich variety of quantum coherent dynamics is found

Theoretical analysis of quantum dynamics in one-dimensional lattices: Wannier-Stark description