Attractive Bose-Einstein condensates in anharmonic traps: Accurate numerical treatment and the intriguing physics of the variance

The dynamics of attractive bosons trapped in one dimensional anharmonic potentials is investigated. Particular emphasis is put on the variance of the position and momentum many-particle operators. Coupling of the center-of-mass and relative-motion degrees-of-freedom necessitates an accurate numerical treatment. The multiconfigurational time-dependent Hartree for bosons (MCTDHB) method is used, and high convergence of the energy, depletion and occupation numbers, and position and momentum variances is proven numerically. We demonstrate for the ground state and out-of-equilibrium dynamics, for condensed and fragmented condensates, for small systems and {it en route} to the infinite-particle limit, that intriguing differences between the density and variance of an attractive Bose-Einstein condensate emerge. Implications are briefly discussed.