2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122719We study analytically and numerically the properties of one-dimensional chain of cold ions placed in a periodic potential of optical lattice and global harmonic potential of a trap. In close similarity with the Frenkel-Kontorova model, a transition from sliding to pinned phase takes place with the increase of the optical lattice potential for the density of ions incommensurate with the lattice period. Quantum fluctuations lead to a quantum phase transition and melting of pinned instanton glass phase at large values of dimensional Planck constant. The obtained results are also relevant for a Wigner crystal placed in a periodic potential.RevTeX, 5 pages, 11 figures, research at http://www.quantware.ups-tlse.frOther Condensed MatterDisordered Systems and Neural NetworksChaotic DynamicsQuantum Physicstext