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Keirstead W.P., Ceccatto H.A., Huberman B.A. — Vibrational Properties of Hierarchical Systems
Keirstead W.P., Ceccatto H.A., Huberman B.A. — Vibrational Properties of Hierarchical Systems

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Название: Vibrational Properties of Hierarchical Systems

Авторы: Keirstead W.P., Ceccatto H.A., Huberman B.A.

Аннотация:

Journal of Statistical Physics, Vol. 53, Nos. 3/4, 1988, p. 733-757.
The vibrational properties of one-dimensional hierarchical systems are investigated and results are obtained for both their eigenvalues and eigenvectors. Two cases are considered, the first one with a hierarchy of spring constants and the latter with a hierarchy in the masses. In both cases the eigenspectrum is found to be a zero-measure, two-scale Cantor set with a fractal dimension between 0 and 1. The scaling properties of the spectra are calculated using renormatization group techniques and are verified by extensive numerical work. The low-frequency density of states and low-temperature specific heat are calculated and a singularity is found in the scaling behavior. The eigenvectors are found to be either extended or critical and self-similar. A transfer matrix formalism is introduced to calculate the scaling properties of the envelope of the critical eigenvectors. Furthermore, a connection is established between the hierarchical vibration and diffusion problems, as well as to the same problems in random systems, thus showing the universality of the observed features.


Язык: en

Рубрика: Физика/

Тип: Статья

Статус предметного указателя: Неизвестно

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 25

Добавлена в каталог: 06.10.2013

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