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

Effective time reversal and echo dynamics in the transverse field Ising model