  We investigate the effect of boundary conditions on spin amplification in
spin chains. We show that the boundaries play a crucial role for the dynamics:
A single additional coupling between the first and last spins can
macroscopically modify the physical behavior compared to the open chain, even
in the limit of infinitely long chains. We show that this effect can be
understood in terms of a "bifurcation" in Hilbert space that can give access to
different parts of Hilbert space with macroscopically different physical
properties of the basis functions, depending on the boundary conditions. On the
technical side, we introduce semiclassical methods whose precision increase
with increasing chain length and allow us to analytically demonstrate the
effects of the boundaries in the thermodynamic limit.
