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تسجيل مستخدم جديدPhonon modes in the Frenkel-Kontorova chain: exponential localization and the number theory properties of frequency bands
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We study numerically phonon modes of the classical one-dimensional Frenkel-Kontorova chain, in the regime of pinned phase characterized by the phonon gap and devils staircase, as well as by a large number of states (configurational excitations), which energy splitting from the ground state is exponentially small. We demonstrate, these states behave like disorder media: their phonon modes are {it exponentially} localized, in contrast to the phonon modes in the ground state, where phonons are {it prelocalized} only. We demonstrate also, the phonon frequency spectrum of the ground state has an hierarchical structure, a direct manifestation of hierarchical spatial structure, found for the ground state of the FK chain in our recent work.
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