The Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons: Theory and Applications

We introduce the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), which represents a unique tool for investigating the nonequilibrium dynamics of multi-species bosonic systems in arbitrary dimensions. Being an ab initio method for solving the time-dependent Schr\"odinger equation, ML-MCTDHB takes all correlations into account. The multi-layer feature of ML-MCTDHB allows for tailoring the wave function ansatz in order to describe intra- and inter-species correlations accurately and efficiently. Examples are shown here to demonstrate the beneficial scaling and the efficiency of the method, especially in the study of nonequilibrium dynamics.