Interacting bosons in external traps: Theory, computational methods and applications beyond standard mean-field

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The experimental realizations of Bose-Einstein condensates (BECs) in ultracold trapped gases have stimulated a modern search for the fundamental physics governing trapped interacting bosons. The most basic theoretical and computational tool for trapped BECs - Gross-Pitaevskii (GP) equation, or, so-called standard mean-field - has been successful in explaining many observations. Yet, the need to go beyond GP is well understood (and documented) by the scientific community; There are many phenomena it cannot explain nor uncover.Recently, utilizing our extended, multi-orbital mean-field approach we have predicted several new physical phenomena. These include the existence and generality of macroscopic fragmentation in the ground and excited states of BECs, a zoo of quantum phases and excitations of bosons in optical lattices, and a rich pathway from condensation via fragmentation to fermionization of trapped cold bosonic systems. The proposed project is aimed at: (1) Continuing the development of our multi-orbital approach, in one- and in higher dimensions, and developing designated many-body tools [self-consistent timeindependent and time-dependent multiconfigurational methods] which are natural extensions of our multi-orbital approach for trapped interacting bosons. (2) Studying the rich physics emerging from the trapping of and manipulating interacting bosons, continuing to predict new physical effects, stimulating experiments and explaining their outcomes. A major goal is to describe the many-body physics accompanying ground and excited-state fragmentation and quantum phase transitions in traps and the many-body dynamics of condensates immersed in different traps and upon their release.