Title: Enhanced mobility of quantum droplets in periodic lattices

Abstract: We predict that one- and two-dimensional self-bound quantum droplets, forming in Bose-Einstein condensates in the presence of Lee-Huang-Yang (LHY) quantum corrections to the mean-field energy, may demonstrate exceptional mobility in periodic optical lattices and that they may exhibit considerable displacements across the lattice, remaining dynamically stable, even under weak initial phase kicks imparted to them. Mobility properties of quantum droplets are determined by their internal structure and strongly depend on the number of particles in them. We find that due to the peculiar effect of the LHY quantum corrections, odd (i.e., on-site centered) and even (i.e., intersite-centered) one-dimensional quantum droplets feature alternating mobility and immobility bands closely corresponding to the regions, where translational perturbation mode is unstable and stable, respectively. This picture becomes even richer in two-dimensional case, where odd-odd, even-odd or even-even quantum droplets also feature alternating mobility and immobility domains, and where, surprisingly, the droplet may be mobile in one direction, but immobile in the orthogonal direction. We link changes in mobility properties with multiple intersections of energy $E(\mu)$ and norm $N(\mu)$ dependencies for droplets with different internal structure.