Phonon modes in the Frenkel-Kontorova chain: exponential localization and the number theory properties of frequency bands

Simple item page
dc.creatorZhirov, O. V.
dc.creatorCasati, G.
dc.creatorShepelyansky, D. L.
dc.date2005-01-10
dc.date.accessioned2026-07-07T03:03:08Z
dc.date.available2026-07-07T03:03:08Z
dc.descriptionWe study numerically phonon modes of the classical one-dimensional Frenkel-Kontorova chain, in the regime of pinned phase characterized by the phonon gap and devil's 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.
dc.description8 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0501188
dc.identifierhttp://arxiv.org/abs/cond-mat/0501188
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/25643
dc.subjectDisordered Systems and Neural Networks
dc.titlePhonon modes in the Frenkel-Kontorova chain: exponential localization and the number theory properties of frequency bands
dc.typetext

Files

Collections

arXiv