1998/01/23 by Walter Schirmacher, W. Schirmacher, Gregor Diezemann +3 · 2 citations
Materials Science · Physics and Astronomy · #Atomic physics #Boson #Condensed matter physics #Hamiltonian (control theory) #Harmonic oscillator #Instability #Lattice (music) #Material Dynamics and Properties #Omega #Physics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physrevlett.81.136
arxiv created 1998/01/23 · openalex publication_date 1998/07/06 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerical diagonalization and by applying the single-bond coherent potential approximation. The results for the density of states g(\ensuremathω) are in excellent agreement with each other. If the system is near the borderline of stability a low-frequency peak appears in the quantity g(\ensuremathω)/\ensuremathω2 as a precursor of the instability. We argue that this peak is the analogon of the ``boson peak,'' observed in structural glasses and other disordered solids. By means of the level distance statistics we show that the peak is not associated with localized states.