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We develop and apply the multi-layer multi-configuration time-dependentHartree method for bosons, which represents an ab initio method forinvestigating the non-equilibrium quantum dynamics of multi-species bosonicsystems. Its multi-layer feature allows for tailoring the wave function ansatzin order to describe intra- and inter-species correlations accurately andefficiently. To demonstrate the beneficial scaling and the efficiency of themethod, we explore the correlated tunneling dynamics of two species withrepulsive intra- and inter-species interactions, to which a third species withvanishing intra-species interaction is weakly coupled. The populationimbalances of the first two species can feature a temporal equilibration andtheir time-evolution significantly depends on the coupling to the thirdspecies. Bosons of the first and of the second species exhibit a bunchingtendency, whose strength can be influenced by their coupling to the thirdspecies.

Non-Equilibrium Quantum Dynamics of Ultra-Cold Atomic Mixtures: the Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons