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We simulate numerically the dynamics of strongly correlated bosons in atwo-leg ladder subject to a time-dependent energy bias between the two chains.When all atoms are initially in the leg with higher energy, we find a drasticreduction of the inter-chain particle transfer for slow linear sweeps, inquantitative agreement with recent experiments. This effect is preceded by arapid broadening of the quasi-momentum distribution of atoms, signaling thepresence of a bath of low-energy excitations in the chains. We furtherinvestigate the scenario of quantum quenches to fixed values of the energybias. We find that for large enough density the momentum distribution relaxesto that of an equilibrium thermal state with the same energy.

Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains