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We analyze the effect of a linear time-variation of the interaction strengthon a trapped one-dimensional Bose gas confined to an optical lattice. Theevolution of different observables such as the experimentally accessible onsiteparticle distribution are studied as a function of the ramp time usingtime-dependent exact diagonalization and density-matrix renormalization grouptechniques. We find that the dynamics of a trapped system typically display tworegimes: for long ramp times, the dynamics are governed by densityredistribution, while at short ramp times, local dynamics dominate as theevolution is identical to that of an homogeneous system. In the homogeneouslimit, we also discuss the non-trivial scaling of the energy absorbed with theramp time.

Slow quench dynamics of a trapped one-dimensional Bose gas confined to an optical lattice