We investigate the heat conductivity $kappa$ of the Heisenberg spin-1/2 ladder at finite temperature covering the entire range of inter-chain coupling $J_perp$, by using several numerical methods and perturbation theory within the framework of linear
response. We unveil that a perturbative prediction $kappa propto J_perp^{-2}$, based on simple golden-rule arguments and valid in the strict limit $J_perp to 0$, applies to a remarkably wide range of $J_perp$, qualitatively and quantitatively. In the large $J_perp$-limit, we show power-law scaling of opposite nature, namely, $kappa propto J_perp^2$. Moreover, we demonstrate the weak and strong coupling regimes to be connected by a broad minimum, slightly below the isotropic point at $J_perp = J_parallel$. As a function of temperature $T$, this minimum scales as $kappa propto T^{-2}$ down to $T$ on the order of the exchange coupling constant. These results provide for a comprehensive picture of $kappa(J_perp,T)$ of spin ladders.
We investigate the occurrence of exponential relaxation in a certain class of closed, finite systems on the basis of a time-convolutionless (TCL) projection operator expansion for a specific class of initial states with vanishing inhomogeneity. It tu
rns out that exponential behavior is to be expected only if the leading order predicts the standard separation of timescales and if, furthermore, all higher orders remain negligible for the full relaxation time. The latter, however, is shown to depend not only on the perturbation (interaction) strength, but also crucially on the structure of the perturbation matrix. It is shown that perturbations yielding exponential relaxation have to fulfill certain criteria, one of which relates to the so-called ``Van Hove structure. All our results are verified by the numerical integration of the full time-dependent Schroedinger equation.
