  We employ the density functional Kohn-Sham method in the local spin-density
approximation to study the electronic structure and magnetism of quasi
one-dimensional periodic arrays of few-electron quantum dots. At small values
of the lattice constant, the single dots overlap, forming a non-magnetic
quantum wire with nearly homogenous density. As the confinement perpendicular
to the wire is increased, i.e. as the wire is squeezed to become more
one-dimensional, it undergoes a spin-Peierls transition. Magnetism sets in as
the quantum dots are placed further apart. It is determined by the electronic
shell filling of the individual quantum dots. At larger values of the lattice
constant, the band structure for odd numbers of electrons per dot indicates
that the array could support spin-polarized transport and therefore act as a
spin filter.
