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“Critical” phonons of the supercritical Frenkel-Kontorova model: Renormalization bifurcation diagrams by Jukka A. Ketoja; Indubala I. Satija is a Physics and Astronomy article available to read on EtoBox.

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The phonon modes of the Frenkel-Kontorova model are studied both at the pinning transition as well as in the pinned (cantorus) phase. We focus on the minimal frequency of the phonon spectrum and the corresponding generalized eigenfunction. Using an exact decimation scheme, the eigenfunctions are shown to have non-trivial scaling properties not only at the pinning transition point but also in the cantorus regime. Therefore the phonons defy localization and remain critical even where the associated area-preserving map has a positive Lyapunov exponent. In this region, the critical scaling properties vary continuously and are described by a line of renormalization limit cycles. Interesting renormalization bifurcation diagrams are obtained by monitoring the cycles as the parameters of the system are varied from an integrable case to the anti-integrable limit. Both of these limits are described by a trivial decimation fixed point. Very surprisingly we find additional special parameter values in the cantorus regime where the renormalization limit cycle degenerates into the above trivial fixed point. At these "degeneracy points" the phonon hull is represented by an infinite series of step

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Author

Jukka A. Ketoja; Indubala I. Satija

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0167-2789)

Published

1997

Language

EN

Field

Physics and Astronomy (Physical Sciences)