Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 42: Critical Phenomena and Phase Transitions

DY 42.2: Talk

Friday, March 18, 2011, 10:30–10:45, ZEU 255

Delocalized-localized transition of disordered phonons — •Sebastian Pinski and Rudolf Römer — Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom

The Anderson model (AM) of localization has been a major topic of research for over 50 years. The resemblance of this model with that of the `scalar' model of phonon localization (SMPL) due to disorder has been noted, yet only probed in 1D systems. Past research on the SMPL has been heavily directed towards the vibrational density of states and unearthing the origins of the boson-peak, with the delocalized-localized transition assumed to be close to the upper band edge. We present work on a equivalence relation between the AM and the SMPL that has enabled direct translation of the electron phase diagram with on-site potential disorder to that of a phonon phase diagram with mass disorder. This has been verified with high accuracy transfer matrix method (TMM) calculations. Phononic phase diagrams for both mass and force-constant disorder in the SMPL are presented for the first time and the implications of these diagrams are discussed. Finally, finite size scaling of the results obtained from TMM indicates that the critical exponent of phononic systems is similar to that of electronic systems.