  Dynamics induced by a change of boundary conditions reveals rate-dependent
signatures associated with topological properties in one-dimensional Kitaev
chain and SSH model. While the perturbation from a change of the boundary
propagates into the bulk, the density of topological edge modes in the case of
transforming to open boundary condition reaches steady states. The steady-state
density depends on the transformation rate of the boundary and serves as an
illustration of quantum memory effects in topological systems. Moreover, while
a link is physically broken as the boundary condition changes, some correlation
functions can remain finite across the broken link and keep a record of the
initial condition. By testing those phenomena in the non-topological regimes of
the two models, none of the interesting signatures of memory effects can be
observed. Our results thus contrast the importance of topological properties in
boundary-induced dynamics.
