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Register a new userEuclidean random matrix theory: low-frequency non-analyticities and Rayleigh scattering
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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 $Z(t)propto t^{(d+2)/2}$.
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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 scattering 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 Matrix Ensembles, which were first introduced in connection with the statistical description of disordered quantum conductors.
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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 inverse 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.
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