Time-dependent multi-orbital mean-field for fragmented Bose–Einstein condensates

The evolution of Bose–Einstein condensates is usually described by the famous time-dependent Gross–Pitaevskii equation, which assumes all bosons to reside in a single time-dependent orbital. In the present work we address the evolution of fragmented condensates, for which two (or more) orbitals are occupied, and derive a corresponding time-dependent multi-orbital mean-field theory. We call our theory TDMF(n), where n stands for the number of evolving fragments. Working equations for a general two-body interaction between the bosons are explicitly presented along with an illustrative numerical example.