Quantum effects in the Frenkel-Kontorova model

We numerically study the quantized verion of the Frenkel-Kontorova model, using Feynman quantization and the Metropolis algorithm. The gross structure of the quantum ground state above the critical parameter value mirrors the classical equilibrium configuration, provided that \ensuremath{\Elzxh} is not too large; nevertheless, its fine structure is significantly different, and can be related to a sawtooth map rather than to the standard map. The dependence of energy on temperature is also investigated and is explained in terms of the quantum phonon spectrum for linearized motion.

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