Coherent structures in the ground state of the quantum Frenkel-Kontorova model

We study the quantum ground state of the Frenkel-Kontorova model in the ''strongly nonlinear'' regime in which in the corresponding classical limit the coordinates of the atoms are distributed on ''Cantori.'' We identify (many) quasidegenerate configurations that contribute to the quantum ground state. When the characteristic quantum and classical energy scales are roughly equal (the ''intermediate'' quantum regime), we find, consistent with earlier numerical studies, that the ''standard map'' determining the coordinates in the classical ground state is renormalized to an effective ''sawtooth'' map, which determines the expectation values of the coordinates in the quantum ground state. We also discuss the dynamics of the model and estimate the characteristic time for various quantum tunneling effects