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We consider the problem of the control of transport in higher dimensionalperiodic structures by applied ac fields. In a generic crystal, transversedegrees of freedom are coupled, and this makes the control of motion difficultto implement. We show, both with simulations and with an analytical functionalexpansion on the driving amplitudes, that the use of quasiperiodic drivingsignificantly suppresses the coupling between transverse degrees of freedom.This allows a precise control of the transport, and does not require a detailedknowledge of the crystal geometry.

Control of transport in higher dimensional systems via dynamical decoupling of degrees of freedom with quasiperiodic driving fields