Renormalization and Quantum Scaling of Frenkel-Kontorova Models

Details Renormalization and Quantum Scaling of Frenkel-Kontorova Models Renormalization and Quantum Scaling of Frenkel-Kontorova Models

2005-01-10

arxiv.org/abs/cond-mat/0501221v1

Physics

Condensed Matter

Statistical Mechanics

14 pages, 1 figure, submitted to J.Stat.Phys

Scientific paper

10.1007/s10955-005-8671-9

We generalise the classical Transition by Breaking of Analyticity for the class of Frenkel-Kontorova models studied by Aubry and others to non-zero Planck's constant and temperature. This analysis is based on the study of a renormalization operator for the case of irrational mean spacing using Feynman's functional integral approach. We show how existing classical results extend to the quantum regime. In particular we extend MacKay's renormalization approach for the classical statistical mechanics to deduce scaling of low frequency effects and quantum effects. Our approach extends the phenomenon of hierarchical melting studied by Vallet, Schilling and Aubry to the quantum regime.

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