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We study the dynamics of a Bose-Einstein condensate (BEC) in a onedimensional optical lattice in the limit of weak atom-atom interactions.Numerically we find that a BEC may develop a pulsating instability in whichatoms nearly periodically collect themselves into a pulse and subsequentlydisperse back into the initial homogeneous state. A qualitative explanation ofthe quasi-periodic behavior is given by drawing an analogy with a double-wellsystem. In an extension we introduce quantum effects approximately withinTruncated Wigner Approximation (TWA). In pure classical mean field theory thecondensate shows an undamped pulsating instability, whereas we have observed adamping in the oscillation when we average over many stochastic realizations.

Classical and quantum dynamics of pulsating instability in a Bose-Einstein condensate in an optical lattice