  Preparing an integrable system in a mixed state described by a thermal
density matrix , we subject it to a sudden quench and explore the subsequent
unitary dynamics. Defining a version of the generalised Loschmidt overlap
amplitude (GLOA) through the purifications of the time evolved density matrix,
we claim that non-analyiticies in the corresponding "dynamical free energy
density" persist and is referred to as mixed state dynamical quantum phase
transitions (MSDQPTs). Furthermore, these MSDQPTs are uniquely characterised by
a topological index constructed by the application of the Pancharatnam geometry
on the purifications of the thermal density matrix; the quantization of this
index however persists up to a critical temperature. These claims are
corroborated analysing the non-equilibrium dynamics of a transverse Ising chain
initially prepared in a thermal state and subjected to a sudden quench of the
transverse field.
