The investigation of the nonequilibrium quantum dynamics of bosonic many-body systems is very challenging due to the excessively growing Hilbert space and poses a major problem for their theoretical description and simulation. We present a novel dynamical pruning approach in the framework of the multi-configuration time-dependent Hartree method for bosons (MCTDHB) to tackle this issue by dynamically detecting the most relevant number states of the underlying physical system and modifying the many-body Hamiltonian accordingly. We discuss two different number state selection criteria as well as two different ways to modify the Hamiltonian. Our scheme regularly re-evaluates the number state selection in order to dynamically adapt to the time evolution of the system. To benchmark our methodology, we study the nonequilibrium dynamics of bosonic particles confined in either an optical lattice or in a double-well potential. It is shown that our approach reproduces the unpruned MCTDHB results accurately while yielding a significant reduction of the simulation time. The speedup is particularly pronounced in the case of the optical lattice.

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