



01780nas a2200181   4500008004100000245006700041210006600108260001500174520113500189653002701324653003101351653004701382653005201429100002201481700003201503700002601535856003701561       2021                        eng d00aRelaxation of non-integrable systems and correlation functions0 aRelaxation of nonintegrable systems and correlation functions  c12/17/20213 a<p>We investigate early-time equilibration rates of observables in closed many-body quantum systems and compare them to those of two correlation functions, first introduced by Kubo and Srednicki. We explore whether these different rates coincide at a universal value that sets the timescales of processes at a finite energy density. We find evidence for this coincidence when the initial conditions are sufficiently generic, or typical. We quantify this with the effective dimension of the state and with a state-observable effective dimension, which estimate the number of energy levels that participate in the dynamics. Our findings are confirmed by proving that these different timescales coincide for dynamics generated by Haar-random Hamiltonians. This also allows to quantitatively understand the scope of previous theoretical results on equilibration timescales and on random matrix formalisms. We approach this problem with exact, full spectrum diagonalization. The numerics are carried out in a non-integrable Heisenberg-like Hamiltonian, and the dynamics are investigated for several pairs of observables and states.</p>10aFOS: Physical sciences10aQuantum Physics (quant-ph)10aStatistical Mechanics (cond-mat.stat-mech)10aStrongly Correlated Electrons (cond-mat.str-el)1 aRiddell, Jonathon1 aGarcía-Pintos, Luis, Pedro1 aAlhambra, Álvaro, M.  uhttps://arxiv.org/abs/2112.09475