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Study of the localization-delocalization transition for phonons via transfer matrix method techniques
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Pinski, S. D. and Römer, Rudolf A. (2011) Study of the localization-delocalization transition for phonons via transfer matrix method techniques. Journal of Physics: Conference Series, Vol.286 (No.1). article no. 012025. doi:10.1088/1742-6596/286/1/012025 ISSN 1742-6596.
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Official URL: http://dx.doi.org/10.1088/1742-6596/286/1/012025
Abstract
We use a transfer-matrix method to study the localization properties of vibrations in a 'mass and spring' model with simple cubic lattice structure. Disorder is applied as a box-distribution to the force-constants k of the springs. We obtain the reduced localization lengths Lambda(M) from calculated Lyapunov exponents for different system widths to roughly locate the squared critical transition frequency omega(2)(c). The data is finite-size scaled to acquire the squared critical transition frequency of omega(2)(c) = 12.54 +/- 0.03 and a critical exponent of nu = 1.55 +/- 0.002.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics Faculty of Science, Engineering and Medicine > Science > Centre for Scientific Computing |
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Library of Congress Subject Headings (LCSH): | Statistical mechanics, Matrices, Anderson model, Lattice dynamics, Phonons | ||||
Journal or Publication Title: | Journal of Physics: Conference Series | ||||
Publisher: | Institute of Physics Publishing Ltd. | ||||
ISSN: | 1742-6596 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Vol.286 | ||||
Number: | No.1 | ||||
Page Range: | article no. 012025 | ||||
DOI: | 10.1088/1742-6596/286/1/012025 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | EP-F040784-1 (EPSRC) | ||||
Version or Related Resource: | Paper presented at the Conference on Condensed Matter and Materials Physics CMMP10, University of Warwick, Coventry, Dec 14-16, 2010. |
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