  Quantum walks often provide telling insights about the structure of the
system on which they are performed. In PT-symmetric and lossy dimer lattices,
the topological properties of the band structure manifest themselves in the
quantization of the mean displacement of such a walker. We investigate the
fragile aspects of a topological transition in these two dimer models. We find
that the transition is sensitive to the initial state of the walker on the
Bloch sphere, and the resultant mean displacement has a robust topological
component and a quasiclassical component. In PT symmetric dimer lattices, we
also show that the transition is smeared by nonlinear effects that become
important in the PT-symmetry broken region. By carrying out consistency checks
via analytical calculations, tight-binding results, and beam-propagation-method
simulations, we show that our predictions are easily testable in today's
experimental systems.
