Exploring local quantum many-body relaxation by atoms in optical superlattices

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For any ε > 0 \varepsilon>0 , t rec > 0 t_{\rm rec}>0 there exists a system size L L and a relaxation time t rel > 0 t_{\rm rel}>0 such that the reduced state satisfies ‖ ϱ ^ I ​ ( t ) − ϱ ^ max ‖ 1 < ε \|\hat{\varrho}_{I}(t)-\hat{\varrho}_{\rm max}\|_{1}<\varepsilon for all t ∈ [ t rel , t rec ] t\in[t_{\rm rel},t_{\rm rec}] [ 2 ]

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For very long times and considerable U U , one may find a relaxation in momentum space due to coupling of eigenmodes, as being corroborated by flow approaches [ 9 ]

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