



01779nas a2200145   4500008004100000245007300041210006900114260001400183490000800197520131100205100002601516700002201542700003201564856003701596       2020                        eng d00aTime evolution of correlation functions in quantum many-body systems0 aTime evolution of correlation functions in quantum manybody syst  c3/19/20200 v1243 a<p>We give rigorous analytical results on the temporal behavior of two-point correlation functions --also known as dynamical response functions or Green&#39;s functions-- in closed many-body quantum systems. We show that in a large class of translation-invariant models the correlation functions factorize at late times &lang;A(t)B&rang;β&rarr;&lang;A&rang;β&lang;B&rang;β, thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that for systems with a generic spectrum the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. For auto-correlation functions we provide an upper bound on the timescale at which they reach the factorized late time value. Remarkably, this bound is only a function of local expectation values, and does not increase with system size. We give numerical examples that show that this bound is a good estimate in non-integrable models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the symmetrized ones and the Kubo function that appears in linear response theory, for which we give analogous results.</p>1 aAlhambra, Álvaro, M.1 aRiddell, Jonathon1 aGarcía-Pintos, Luis, Pedro  uhttps://arxiv.org/abs/1906.11280