Coherent potential approximation for diffusion and wave propagation in topologically disordered systems
Using Gaussian integral transform techniques borrowed from functional-integral field theory and the replica trick we derive a version of the coherent potential approximation (CPA) suited for describing (i) the diffusive (hopping) motion of classical particles in a random environment, and (ii) the vi...
Gespeichert in:
Veröffentlicht in: | Physical review. B, Condensed matter and materials physics Condensed matter and materials physics, 2013-08, Vol.88 (6), Article 064203 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | Using Gaussian integral transform techniques borrowed from functional-integral field theory and the replica trick we derive a version of the coherent potential approximation (CPA) suited for describing (i) the diffusive (hopping) motion of classical particles in a random environment, and (ii) the vibrational properties of materials with spatially fluctuating elastic coefficients in topologically disordered materials. The effective medium in the present version of the CPA is not a lattice but a homogeneous and isotropic medium, representing an amorphous material on a mesoscopic scale. The transition from a frequency-independent to a frequency-dependent diffusivity (conductivity) is shown to correspond to the boson peak in the vibrational model. The anomalous regimes above the crossover are governed by a complex, frequency-dependent self-energy. The boson peak is shown to be stronger for non-Gaussian disorder than for Gaussian disorder. We demonstrate that the low-frequency nonanalyticity of the off-lattice version of the CPA leads to the correct long-time tails of the velocity autocorrelation function in the hopping problem and to low-frequency Rayleigh scattering in the wave problem. Furthermore we show that the present version of the CPA is capable of treating the percolative aspects of hopping transport adequately. |
---|---|
ISSN: | 1098-0121 1550-235X |
DOI: | 10.1103/PhysRevB.88.064203 |