Lushuai Cao, Sven Krönke, Oriol Vendrell, Peter Schmelcher
In this work, a generalization of the multi-configuration time-dependent Hartree method (MCTDH) is presented, which we call multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB). ML-MCTDHB is a variational ab initio method for solving the time-dependent many-body Schr\"odinger equation for bosonic systems. It combines the efficiency of the MCTDH method for bosons (MCTDHB) with the tailored wave function ansatz of multi-layer MCTDH (ML-MCTDH), which is guided by system specific correlations. Here, we show that such a symbiosis is possible for two classes of wave function ansatzes and any combination thereof: (i) In a bosonic multi-species setting, a multi-layer expansion can be employed in order to tailor the wave function ansatz according to the strengths of inter- and intra-species correlations. (ii) In the case of bosons in two or three dimensions or bosons with internal degrees of freedom, the multi-layer expansion allows for efficiently representing the high-dimensional single particle orbitals. In particular, the latter is useful for quasi one- or quasi two-dimensional trap geometries. Apart from developing the theoretical framework of ML-MCTDHB, we demonstrate its power and efficiency by means of several relevant numerical examples.
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http://arxiv.org/abs/1210.8063
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