We develop the multi-layer multi-configuration time-dependent Hartree method for bosons (ML-MCTDHB), a variational numerically exact ab initio method for studying the quantum dynamics and stationary properties of general bosonic systems. ML-MCTDHB takes advantage of the permutation symmetry of identical bosons, which allows for investigations of the quantum dynamics from few to many-body systems. Moreover, the multi-layer feature enables ML-MCTDHB to describe mixed bosonic systems consisting of arbitrary many species. Multi-dimensional as well as mixed-dimensional systems can be accurately and efficiently simulated via the multi-layer expansion scheme. We provide a detailed account of the underlying theory and the corresponding implementation. We also demonstrate the superior performance by applying the method to the tunneling dynamics of bosonic ensembles in a one-dimensional double well potential, where a single-species bosonic ensemble of various correlation strengths and a weakly interacting two-species bosonic ensemble are considered.
The multi-layer multi-configuration time-dependent Hartree method for bosons: Theory, implementation, and applications
Lushuai Cao, Sven Krönke, Oriol Vendrell, Peter Schmelcher; The multi-layer multi-configuration time-dependent Hartree method for bosons: Theory, implementation, and applications. J. Chem. Phys. 7 October 2013; 139 (13): 134103. https://doi.org/10.1063/1.4821350
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