Slow relaxation and sensitivity to disorder in trapped lattice fermions after a quench

M.S. acknowledges support from Engineering and Physical Sciences Research Council (EPSRC) (United Kingdom) via the CM-CDT program, Grant No. EP/L015110/1. C.A.H.’s work on this paper was performed in part at the Aspen Center for Physics, which is supported by NSF Grant No. PHY-1066293. He is grateful to them for their hospitality. He is also thankful for ongoing support from the EPSRC (United Kingdom) via the TOPNES program, Grant No. EP/I031014/1.We consider a system of non-interacting fermions in one dimension subject to a single-particle potential consisting of (a) a strong optical lattice, (b) a harmonic trap, and (c) uncorrelated on-sited is order. After a quench, in which the center of the harmonic trap is displaced, we study the occupation function of the fermions and the time-evolution of experimental observables. Specifically, we present numerical and analytical results for the post-quench occupation function of the fermions,and analyse the time-evolution of the real-space density profile. Unsurprisingly for a non-interacting(and therefore integrable) system, the infinite-time limit of the density profile is non-thermal. However,due to Bragg-localization of the higher-energy single-particle states, the approach to even this non-thermal state is extremely slow. We quantify this statement, and show that it implies a sensitivity to disorder parametrically stronger than that expected from Anderson localization.PostprintPeer reviewe