Irreversibility, despite being a necessary condition for thermalization, still lacks a sound understanding in the context of isolated quantum many-body systems. In this Rapid Communication we approach this question by studying the behavior of generic many-body systems under imperfect effective time reversal, where the imperfection is introduced as a perturbation of the many-body state at the point of time reversal. Based on numerical simulations of the full quantum dynamics we demonstrate that observable echoes occurring in this setting decay exponentially with a rate that is independent of the perturbation; hence, the sensitivity to perturbations is intrinsic to the system, meaning that the dynamics is effectively irreversible.

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• Cold gases in optical lattices
• Entanglement production
• Quantum chaos
• Quantum correlations, foundations & formalism
• Quantum statistical mechanics