We want to explore static and dynamic behaviour of cold atoms in periodic and quasi-periodic potentials, with emphasis on ultradilute droplets. Quantum fluctuations in these systems are only starting to be explored, and we expect new phases to be uncovered. We plan also to study dynamics after quenching lattice potential or interaction to understand the role of interactions in quasi-periodic systems far from equilibrium. Non-equilibrium many-body physics has become the focus of many quantum gas experiments and tVMC is ideally suited to simulate them. For chosen systems we will determine the changes of phase diagram with temperature, which will besides the community of ultracold atoms give valuable insight to the community studying adsorption of quantum fluids on substrates.