We give rigorous analytical results on the temporal behavior of two-point correlation functions-also known as dynamical response functions or Green{\textquoteright}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 \< A(t)B \>(beta) -\> \< A \>(beta) \< B \>(beta) , 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 autocorrelation 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 nonintegrable models, and argue that the timescale that appears can be understood in terms of an emergent fluctuationdissipation 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.

}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.124.110605}, author = {Alhambra, Alvaro M. and Riddell, Jonathon and Garcia-Pintos, Luis Pedro} } @article {nicholson_time-information_2020, title = {Time-information uncertainty relations in thermodynamics}, journal = {Nat. Phys.}, volume = {16}, number = {12}, year = {2020}, note = {Place: HEIDELBERGER PLATZ 3, BERLIN, 14197, GERMANY Publisher: NATURE RESEARCH Type: Article}, month = {dec}, abstract = {Physical systems powering motion and creating structure in a fixed amount of time dissipate energy and produce entropy. Whether living, synthetic or engineered, 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 s.d. From this general bound, we establish a family of speed limits for heat, dissipated/chemical work and entropy depending on the experimental constraints on the system and its environment. In all of these inequalities, the timescale 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 constraints on the stochastic dynamics or their function. A time-information uncertainty relation in thermodynamics has been derived, analogous to the time-energy uncertainty relation in quantum mechanics, imposing limits on the speed of energy and entropy exchange between a system and external reservoirs.}, issn = {1745-2473}, doi = {10.1038/s41567-020-0981-y}, author = {Nicholson, Schuyler B. and Garcia-Pintos, Luis Pedro and del Campo, Adolfo and Green, Jason R.} }