ترغب بنشر مسار تعليمي؟ اضغط هنا

Euclidean random matrix theory: low-frequency non-analyticities and Rayleigh scattering

191   0   0.0 ( 0 )
 نشر من قبل Walter Schirmacher
 تاريخ النشر 2010
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

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 $Z(t)propto t^{(d+2)/2}$.



قيم البحث

اقرأ أيضاً

254 - Z. Voros , G. Weihs 2014
In this paper we theoretically study how structural disorder in coupled semiconductor heterostructures influences single-particle scattering events that would otherwise be forbidden by symmetry. We extend the model of V. Savona to describe Rayleigh s cattering in coupled planar microcavity structures, and answer the question, whether effective filter theories can be ruled out. They can.
Theory of Random Matrix Ensembles have proven to be a useful tool in the study of the statistical distribution of energy or transmission levels of a wide variety of physical systems. We give an overview of certain q-generalizations of the Random Matr ix Ensembles, which were first introduced in connection with the statistical description of disordered quantum conductors.
We consider the additive superimposition of an extensive number of independent Euclidean Random Matrices in the high-density regime. The resolvent is computed with techniques from free probability theory, as well as with the replica method of statist ical physics of disordered systems. Results for the spectrum and eigenmodes are shown for a few applications relevant to computational neuroscience, and are corroborated by numerical simulations.
We present a simple, perturbative approach for calculating spectral densities for random matrix ensembles in the thermodynamic limit we call the Perturbative Resolvent Method (PRM). The PRM is based on constructing a linear system of equations and ca lculating how the solutions to these equation change in response to a small perturbation using the zero-temperature cavity method. We illustrate the power of the method by providing simple analytic derivations of the Wigner Semi-circle Law for symmetric matrices, the Marchenko-Pastur Law for Wishart matrices, the spectral density for a product Wishart matrix composed of two square matrices, and the Circle and elliptic laws for real random matrices.
162 - V.E.Kravtsov 2009
This is a course on Random Matrix Theory which includes traditional as well as advanced topics presented with an extensive use of classical logarithmic plasma analogy and that of the quantum systems of one-dimensional interacting fermions with invers e square interaction (Calogero-Sutherland model). Certain non-invariant random matrix ensembles are also considered with the emphasis on the eigenfunction statistics in them. The course can also be viewed as introduction to theory of localization where the (non-invariant) random matrix ensembles play a role of the toy models to illustrate functional methods based on super-vector/super-matrix representations.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا