6533b85afe1ef96bd12b9813
RESEARCH PRODUCT
Euclidean random matrix theory: low-frequency non-analyticities and Rayleigh scattering
Walter SchirmacherCarl Gantersubject
PhysicsDensity matrixStatistical Mechanics (cond-mat.stat-mech)AutocorrelationFOS: Physical sciencesInverseDisordered Systems and Neural Networks (cond-mat.dis-nn)Condensed Matter - Disordered Systems and Neural Networks16. Peace & justiceCondensed Matter Physics01 natural sciences010305 fluids & plasmassymbols.namesakeSelf-energyTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYQuantum mechanicsPhysical Sciences0103 physical sciencesEuclidean geometrysymbolsRayleigh scatteringDiffusion (business)010306 general physicsRandom matrixCondensed Matter - Statistical Mechanicsdescription
By calculating all terms of the high-density expansion of the euclidean random matrix theory (up to second-order in the inverse density) for the vibrational spectrum of a topologically disordered system we show that the low-frequency behavior of the self energy is given by $\Sigma(k,z)\propto k^2z^{d/2}$ and not $\Sigma(k,z)\propto k^2z^{(d-2)/2}$, as claimed previously. This implies the presence of Rayleigh scattering and long-time tails of the velocity autocorrelation function of the analogous diffusion problem of the form $Z(t)\propto t^{(d+2)/2}$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-01-11 | Philosophical Magazine |