The atomic ground state density at the nucleus is bounded from above by a certain explicitly given positive constant times the third power of the nuclear charge.

The integrable loop model with mixed boundary conditions based on the 1-boundary extended Temperley–Lieb algebra with loop weight 1 is considered. The corresponding qKZ equation is introduced and its minimal degree solution described. As a result, the sum of the properly normalized components of the ground state in size L is computed and shown to be equal to the number of Horizontally and Verti...

We investigate the ground state of a system of interacting particles in small nonlinear lattices with M >or=3 sites, using as a prototypical example the discrete nonlinear Schrödinger equation that has been recently used extensively in the contexts of nonlinear optics of waveguide arrays and Bose-Einstein condensates in optical lattices. We find that, in the presence of attractive interactions,...

In this paper, we propose a new numerical method to compute the ground-state solution of trapped interacting Bose–Einstein condensation at zero or very low temperature by directly minimizing the energy functional via finite element approximation. As preparatory steps we begin with the 3d Gross–Pitaevskii equation (GPE), scale it to get a three-parameter model and show how to reduce it to 2d and...

In this paper, we propose a new numerical method to compute the ground state solution of trapped interacting Bose-Einstein condensation (BEC) at zero or very low temperature by directly minimizing the energy functional via finite element approximation. As preparatory steps we begin with the 3d Gross-Pitaevskii equation (GPE), scale it to get a three-parameter model and show how to reduce it to ...