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When it comes to applying the adiabatic theorem in practice, the key questionto be answered is how slow "slowly enough" is. This question can be anintricate one, especially for many-body systems, where the limits of slowdriving and large system size may not commute. Recently we have shown how thequantum adiabaticity in many-body systems is related to the generalizedorthogonality catastrophe [Phys. Rev. Lett. 119, 200401 (2017)]. We have provena rigorous inequality relating these two phenomena and applied it to establishconditions for the quantized transport in the topological Thouless pump. In thepresent contribution we (i) review these developments and (ii) apply theinequality to establish the conditions for adiabaticity in a one-dimensionalsystem consisting of a quantum fluid and an impurity particle pulled throughthe fluid by an external force. The latter analysis is vital for the correctquantitative description of the phenomenon of quasi Bloch oscillations in aone-dimensional translation invariant impurity-fluid system.

Quantum Many-Body Adiabaticity, Topological Thouless Pump and Driven Impurity in a One-Dimensional Quantum Fluid