We study the interaction-induced connectivity in the Fock space of two particles in a disordered one-dimensional potential. Recent computational studies showed that the largest localization length $xi_2$ of two interacting particles in a weakly rando
m tight binding chain is increasing unexpectedly slow relative to the single particle localization length $xi_1$, questioning previous scaling estimates. We show this to be a consequence of the approximate restoring of momentum conservation of weakly localized single particle eigenstates, and disorder-induced phase shifts for partially overlapping states. The leading resonant links appear among states which share the same energy and momentum. We substantiate our analytical approach by computational studies for up to $xi_1 = 1000$. A potential nontrivial scaling regime sets in for $ xi_1 approx 400$, way beyond all previous numerical attacks.
We study the spreading of single-site excitations in one-dimensional disordered Klein-Gordon chains with tunable nonlinearity $|u_{l}|^{sigma} u_{l}$ for different values of $sigma$. We perform extensive numerical simulations where wave packets are e
volved a) without and, b) with dephasing in normal mode space. Subdiffusive spreading is observed with the second moment of wave packets growing as $t^{alpha}$. The dependence of the numerically computed exponent $alpha$ on $sigma$ is in very good agreement with our theoretical predictions both for the evolution of the wave packet with and without dephasing (for $sigma geq 2$ in the latter case). We discuss evidence of the existence of a regime of strong chaos, and observe destruction of Anderson localization in the packet tails for small values of $sigma$.
