  We have studied the dynamical thermal effects on the protected end states of
a topological insula- tor (TI) when it is considered as an open quantum system
in interaction with a noisy environment at a certain temperature T . As a
result, we find that protected end states in a TI become unstable and decay
with time. Very remarkably, the interaction with the thermal environment
(fermion-boson) respects chiral symmetry, which is the symmetry responsible for
the protection (robustness) of the end states in this TI when it is isolated
from the environment. Therefore, this mechanism makes end states unstable while
preserving their protecting symmetry. Our results have immediate practical
implications in recently proposed simulations of TI using cold atoms in optical
lattices. Accordingly, we have computed lifetimes of topological end states for
these physical implementations that are useful to make those experiments
realistic.
