Examples
Selected applications of the MCTDHB

Generic quantum manybody dynamics of trapped strongly repulsive Bose systems with finite/long range interactions (movie 1, 2D);
(movie 2, 2D);
(movie 3, 3D);
(movie 4, 3D).
Evolutions of a twohump twofold fragmented initial state in 2D and 3D induced by a sudden displacement of the trap along with a simultaneous quench of the interparticle repulsion (computed with MCTDHB). Strong decrease of the interaction leads to `overabarrier' dynamics (movies 1 and 3), whereas moderate increase of the interaction leads to `underabarrier' dynamics (movies 2 and 4). The concept of interactioninduced timedependent barriers, used to explain the two generic dynamical regimes, is visualized in 2D (movies 1 and 2). For more details, see:
Generic regimes of quantum manybody dynamics of trapped bosonic systems with strong repulsive interactions, O. I. Streltsova, O. E. Alon, L. S. Cederbaum, A. I. Streltsov, arXiv:1312.6174v1 [condmat.quantgas]. 
Buildup of correlations and wave chaos in a BEC expanding in a
1D periodic potential (movie).
A weakly interacting BEC is prepared in the ground state of a 1D harmonic potential. The potential is then switched off and the BEC is allowed to expand in a shallow periodic potential. The movie shows the twoparticle normalized correlation function g^{(2)}(x_{1},x_{2},x_{1},x_{2},t) as well as the (scaled) density of the second natural orbital as a function of time (computed with MCTDHB). The BEC is initially almost perfectly coherent. Deviations from g^{(2)}=1 emerge at about t=3t_{0}. This onset of depletion and loss of coherence on the manybody level is in close correspondence with the onset of wave chaos in the GrossPitaevskii equation, that is, the onset of exponential separation in Hilbert space of two nearby condensate wave functions. For more details, see:
Wave chaos as signature for depletion of a BoseEinstein condensate, I. Brezinová, A. U. J. Lode, A. I. Streltsov, O. E. Alon, L. S. Cederbaum, and J. Burgdörfer, Phys. Rev. A 86, 013603 (2012), arXiv:1202.5869. 
Fewboson decaybytunneling and fragmentation (movie 1);
(movie 2).
Two weakly interacting bosons are prepared in an harmonic trap. When the trap is made open such that the bosons can tunnel out, the initiallycoherent twoboson system becomes fragmented. The fragmentation manifests itself with the emergence of a pronounced twopeak structure in momentum space (computed with MCTDHB, see movie 1) and the correlation function g(x'_{1},x_{1},t)^{2} differing from 1 (computed with MCTDHB, see movie 2). The corresponding GrossPitaevskii dynamics, where the system remains coherent at all times, exhibits a singlepeak structure in momentum space and has g(x'_{1},x_{1},t)^{2}=1 (not shown). For more details, see:
Mechanism of Tunneling in Interacting Open Ultracold FewBoson Systems, A. U. J. Lode, A. I. Streltsov, O. E. Alon, L. S. Cederbaum, arXiv:1005.0093v1 [condmat.quantgas]. 
Exact manybody dynamics of a bosonic Josephson junction (movie).
In a bosonic Josephson junction the density tunnels from one side of the junction to the other. The repulsive interaction between the particles can lead to an effect known as selftrapping, a large increase in the time needed for the bosons to tunnel through the potential barrier from a certain (repulsive) interaction strength onwards. Here we compare the bosonic Josephson junction dynamics of 100 bosons based on two approaches: the numerically exact solution of the timedependent manybody Schrödinger equation obtained using the MCTDHB algorithm, and the respective result based on the BoseHubbard model. The selftrapping effect can be seen in both results, but the exact dynamics is very different from that of the BoseHubbard model. Shown is the density of the condensate. For more details, see:
Exact quantum dynamics of a bosonic Josephson junction, K. Sakmann, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Phys. Rev. Lett. 103, 220601 (2009), arXiv:0905.0902. 
Fragmenton formation (movie).
Formation of a dynamicallystable fragmented object termed Fragmenton in 1D attractive Bose gases. Given a groundstate bright soliton, making the interaction suddenly more attractive (here by a factor of four) leads to the breakup of the bright soliton into two subclouds, signifying the birth of the Fragmenton. The phenomenon is seen on the manybody level (computed with MCTDHB), whereas on the GrossPitaevskii meanfield level, which assumes all bosons to remain coherent at all times, it does not occur. For more details, see:
Formation and Dynamics of ManyBoson Fragmented States in OneDimensional Attractive Ultracold Gases, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Phys. Rev. Lett. 100, 130401 (2008), arXiv:0711.2778.