Number fluctuations of cold spatially split bosonic objects

We investigate the number fluctuations of spatially split many-boson systems employing a theorem about the maximally and minimally attainable variances of an observable. The number fluctuations of many-boson systems are given for different numbers of lattice sites and both mean-field and many-body wave functions. It is shown which states maximize the particle number fluctuations, both in lattices and double-wells. The fragmentation of the states is discussed, and it is shown that the number fluctuations of some fragmented states are identical to those of fully condensed states.