Collective dynamics of atomic systems with dipolar interactions in ladder geometries

In connection with recent experiments with ultracold atoms, in my thesis I will discuss the low-energy spectrum and out-of-equilibrium dynamics of hard-core bosons with nearest-neighbor repulsion in one-dimensional and ladder geometries. At half filling and in the regime $V\gg J$, the ground state is a density wave; hole doping creates a localized defect that propagates as a quasi-particle, whose internal structure consists of two confined domain walls. Using degenerate perturbation theory, we derive analytic dispersion relations that quantitatively reproduce exact diagonalization results. On the ladder, the inter leg hopping splits the lowest band into two branches, producing an oscillation of the defect between the two legs. The hard-core analysis is validated for $U/V \gtrsim 1.5$ where the predictions are directly testable.