



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/1906.1128001726nas a2200145   4500008004100000245006100041210006000102260001500162520126300177100002801440700003201468700002201500700002101522856003701543       2020                        eng d00aTime-information uncertainty relations in thermodynamics0 aTimeinformation uncertainty relations in thermodynamics  c09/21/20203 a<p>Physical systems that power motion and create structure in a fixed amount of time dissipate energy and produce entropy. Whether living or synthetic, systems performing these dynamic functions must balance dissipation and speed. Here, we show that rates of energy and entropy exchange are subject to a speed limit -- a time-information uncertainty relation -- imposed by the rates of change in the information content of the system. This uncertainty relation bounds the time that elapses before the change in a thermodynamic quantity has the same magnitude as its initial standard deviation. From this general bound, we establish a family of speed limits for heat, work, entropy production, and entropy flow depending on the experimental constraints on the system. In all of these inequalities, the time scale of transient dynamical fluctuations is universally bounded by the Fisher information. Moreover, they all have a mathematical form that mirrors the Mandelstam-Tamm version of the time-energy uncertainty relation in quantum mechanics. These bounds on the speed of arbitrary observables apply to transient systems away from thermodynamic equilibrium, independent of the physical assumptions about the stochastic dynamics or their function.&nbsp;</p>1 aNicholson, Schuyler, B.1 aGarcía-Pintos, Luis, Pedro1 adel Campo, Adolfo1 aGreen, Jason, R.  uhttps://arxiv.org/abs/2001.05418