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We explore the effect of transverse confinement on the stability of aBose-Einstein condensate (BEC) loaded in a shaken one-dimensional ortwo-dimensional square lattice. We calculate the decay rate from two-particlecollisions. We predict that if the transverse confinement exceeds a criticalvalue, then, for appropriate shaking frequencies, the condensate is stableagainst scattering into transverse directions.

Stability of a Bose-Einstein condensate in a driven optical lattice: Crossover between weak and tight transverse confinement