2007/11/08 by W. Schirmacher, Walter Schirmacher, B. Schmid +7 · 65 citations
Materials Science · Mathematics · Physics and Astronomy · #Boson #Brillouin zone #Condensed matter physics #Geometry #Instability #Lattice (music) #Material Dynamics and Properties #Mathematics #Physics #Quantum mechanics #Random lasers and scattering media #Scaling #Square lattice #Statistical physics #Statistics #Theoretical and Computational Physics #Uncorrelated #Wavenumber #cond-mat.dis-nn #cond-mat.other
paper · pdf · doi:10.1002/pssc.200777584
published in Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics 5(3), 862-866 (Wiley) · 5 pages, 3 figures, to be published in physica status solidi (c) March 2008
arxiv created 2007/11/08 · openalex publication_date 2008/02/06 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract We investigate a d ‐dimensional model ( d = 2,3) for sound waves in a disordered environment, in which the local fluctuations of the elastic modulus are spatially correlated with a certain correlation length. The model is solved analytically by means of a field‐theoretical effective‐medium theory (self‐consistent Born approximation) and numerically on a square lattice. As in the uncorrelated case the theory predicts an enhancement of the density of states over Debye's ω d –1 law (“boson peak”) as a result of disorder. This anomay becomes reinforced for increasing correlation length ξ . The theory predicts that ξ times the width of the Brillouin line should be a universal function of ξ times the wavenumber. Such a scaling is found in the 2 d simulation data, so that they can be represented in a universal plot. In the low‐wavenumber regime, where the lattice structure is irrelevant there is excellent agreement between the simulation at small disorder. At larger disorder the continuum theory deviates from the lattice simulation data. It is argued that this is due to an instability of the model with stronger disorder. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)