Regensburg 2010 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 6: Poster Session I

DY 6.56: Poster

Montag, 22. März 2010, 16:00–18:00, Poster B2

Study of the delocalised-localised critical transition frequency for phonons — •Sebastian Pinski and Rudolf Römer — University of Warwick, Coventry, CV4 7AL, United Kingdom

In electronic systems, unlike phononic, the mobility edge of disordered electrons is well known for the Anderson model of localization. In phononic cases it is widely believed that a similar transition exists, although evidence is slim and has been achieved mostly through the Coherent Potential Approximation. We introduce a direct diagonalisation routine to obtain all vibrational eigenmodes frequencies of a three-dimensional mass and spring model under varying degree of disorder. We find the Participation Ratios and Vibrational Density of States for system sizes L= 6, 8, 10, 12 and 15 and disorders whilst averaging over 2000 realisations for all disorder magnitudes. Preliminary results suggest that the delocalised-localised transition must exist very close to the upper end of the spectrum for all mass and spring disorders considered. A natural extension to this work is to employ the transfer matrix method to find the Lyapunov exponents of quasi one-dimensional phononic systems which should reveal an exact transition frequency.