Dresden 2011 – wissenschaftliches Programm

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DF: Fachverband Dielektrische Festkörper

DF 11: Glasses I (Joint Session of DY, DF, CPP)

DF 11.1: Vortrag

Mittwoch, 16. März 2011, 10:15–10:30, KÖN Farb

Boson-peak in glasses and random-matrix statistics — •Walter Schirmacher — Institut für Physik, Univ. Mainz — Physik-Department E13, TU München

The enhancement of the vibrational density of states (DOS) with respect to the Debye expectation (``boson peak''), which is universally observed in glasses, is considered by means of of symmetry arguments. Low-frequency wave-like excitations in a disordered solids probe a homogeneous and isotropic material. Due to these symmetries the vibrational wave-like states are highly degenerate (Debye regime). This degeneracy is lifted at higher frequencies. In this regime the discretized equation of motions are governed by a sparse random matrix. The eigenvalues of this matrix are non-degenerate and show the distance statistics of the Gaussian orthogonal ensemble (``level repulsion''). It is conjectured that the integrated density of levels in this regime increases linearly. The cross-over from the Debye regime to the random-matrix regime leads in three dimensions to an enhancement of the DOS. In two dimensions this is not the case. Model calculations using a field-theoretical approach [1] and inspection of simulation data [2] confirm this reasoning.

[1] W. Schirmacher, Europhys. Lett. Europhysics Letters, 73, 892 (2006); [2] see e.g. S. K. Sarkar, G. S. Matharoo, A. Pandey, Phys. Rev. Lett. 92,215503 (2004)