  The question of thermalisation in closed quantum many-body systems has
received a lot of attention in the past few years. An intimately related
question is whether a closed quantum system shows irreversible dynamics.
However, irreversibility and what we actually mean by this in a quantum
many-body system with unitary dynamics has been explored very little. In this
work we investigate the dynamics of the Ising model in a transverse magnetic
field involving an imperfect effective time reversal. We propose a definition
of irreversibility based on the echo peak decay of observables. Inducing the
effective time reversal by different protocols we find algebraic decay of the
echo peak heights or an ever persisting echo peak indicating that the dynamics
in this model is well reversible.
