Rugged landscapes and the ''Quantori'' ground state of 1D quantum systems of adatoms on substrates

We study the landscape of the ground state (''Quantori'') of the quantum Frenkel-Kontorova (FK) model in the ''strong coupling'' regime in which in the corresponding classical limit the coordinates of the atoms are distributed on ''Cantori''. For the intermediate quantum regime, defined as the region in which the natural quantum energy scale and the natural classical energy scale are comparable, we find that many-particle tunneling among numerous, nearly degenerate, inhomogeneous classical configurations (reflecting the ''rugged landscape'' of the problem) leads to a renormalization of the dynamical system used to determine the ground state. In particular, the ''standard map'' which normally arises in the determination of the ground state of the classical FK model is replaced by an effective ''sawtooth map'' to determine the quantum ground state. We discuss the region of parameters for possible realization of the ''Quantori'' ground slate in experiments with adatoms on substrates.