Given a quantum many-body system and the expectation-value dynamics of some operator, we study how this reference dynamics is altered due to a perturbation of the system's Hamiltonian. Based on projection operator techniques, we unveil that if the perturbation exhibits a random-matrix structure in the eigenbasis of the unperturbed Hamiltonian, then this perturbation effectively leads to an exponential damping of the original dynamics. Employing a combination of dynamical quantum typicality and numerical linked cluster expansions, we demonstrate that our theoretical findings for random matrices can, in some cases, be relevant for the dynamics of realistic quantum many-body models as well. Specifically, we study the decay of current autocorrelation functions in spin-1/2 ladder systems, where the rungs of the ladder are treated as a perturbation to the otherwise uncoupled legs. We find a convincing agreement between the exact dynamics and the lowest-order prediction over a wide range of interchain couplings.

The dynamics of magnetization and energy densities are studied in the two-leg spin-1/2 ladder. Using an efficient pure-state approach based on the concept of typicality, we calculate spatio-temporal correlation functions for large systems with up to 40 lattice sites. In addition, two subsequent Fourier transforms from real to momentum space as well as from time to frequency domain yield the respective dynamical structure factors. Summarizing our main results, we unveil the existence of genuine diffusion both for spin and energy. In particular, this finding is based on four distinct signatures which can all be equally well detected: (i) Gaussian density profiles, (ii) time-independent diffusion coefficients, (iii) exponentially decaying density modes, and (iv) Lorentzian line shapes of the dynamical structure factor. The combination of (i) -(iv) provides a comprehensive picture of high-temperature dynamics in this archetypal nonintegrable quantum model. * jonasrichter@uos.de † rsteinig@uos.de 2 3 µ Re σ(ω)/β J ⊥ = 0.5 J ⊥ = 1.0 J ⊥ = 2.0 Ø ÅÊ Re κ(ω)/β 2 ω J ⊥ = 1.0 J ⊥ = 2.0

Concepts like "typicality" and the "eigenstate thermalization hypothesis" aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in which this equilibrium is approached. Our point of departure is the (evident) observation that some forms of the approach to equilibrium, such as, e.g., exponential decay of observables, are much more common then others. We suggest to trace this dominance of certain decay dynamics back to a larger stability with respect to generic Hamiltonian perturbations. A numerical study of a number of examples in which both, the unperturbed Hamiltonians as well as the perturbations are modelled by partially random matrices is presented. We furthermore develop a simple heuristic, mathematical scheme that describes the result of the numerical investigations remarkably well. According to those investigations the exponential decay indeed appears to be most stable. Dynamics that are in a certain sense at odds with the arrow of time are found to be very unstable.

We consider closed quantum systems (into which baths may be integrated) that are driven, i.e., subject to time-dependent Hamiltonians. Our point of departure is the assumption that if systems start in non-Gibbsian states at some initial energies, the resulting probability distributions of work may be largely independent of the specific initial energies. It is demonstrated that this assumption has some far-reaching consequences, e.g., it implies the validity of the Jarzynski relation for a large class of non-Gibbsian initial states. By performing numerical analysis on integrable and nonintegrable spin systems, we find the above assumption fulfilled for all examples considered. Through an analysis based on Fermi's golden rule, we partially relate these findings to the applicability of the eigenstate thermalization ansatz to the respective driving operators.

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