arXiv subjects
Publications and source records attributed to Aris L. Moustakas.
Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B positive definite (square) matrices of arbitrary dimensions. Such so-called ``correlated Wishart matrices'' occur in many fields ranging from information theory to multivariate analysis.
Coherent wave propagation in disordered media gives rise to many fascinating phenomena as diverse as universal conductance fluctuations in mesoscopic metals and speckle patterns in light scattering. Here, the theory of electromagnetic wave propagation in diffusive media is combined with information theory to show how interference affects the information transmission rate between antenna arrays. Nontrivial dependencies of the information capacity on the nature of the antenna arrays are found, such as the dimensionality of the arrays and their direction with respect to the local scattering medium. This approach provides a physical picture for understanding the importance of scattering in the transfer of information through wireless communications.
Tunnelling impurities in metals have been known for some time to have the potential for exhibiting Kondo-like physics. However previous models based on an impurity hopping between two equivalent positions have run into trouble due to the existence of relevant operators that drive the system away from the non-Fermi-liquid Kondo fixed point. In the case of an impurity hopping among positions with higher symmetry, such as triangular symmetry, it is shown here that the non-Fermi-liquid behavior at low temperatures can be generic. Using various bosonization techniques, the fixed point is shown to be {\em stable}. However, unlike the conventional two-channel Kondo (2CK) model, it has {\em four} leading irrelevant operators, implying that while the form of the singular temperature dependence of physical quantities is similar to the 2CK model, there will not be simple universal amplitude ratios. The phase diagram of this system is analyzed and a critical manifold is found to separate the non-Fermi-liquid from a conventional Fermi liquid fixed point. Generalization to higher symmetries, such as cubic, and the possibility of physical realizations with dynamic Jahn-Teller impurities is discussed.
It has been claimed that an impurity hopping between two sites in a metal can lead to non--Fermi liquid behavior if the bias between the two sites is tuned to zero. Here it is shown that several extra tunnelling processes are allowed; those involving bare impurity tunnelling as well as two--electron--assisted tunnelling play important roles. These terms generally drive the system away from the intermediate coupling non--Fermi--liquid fixed point, which has the character of the two channel Kondo problem. In order to find the non-Fermi liquid behavior a combination of these terms must be small over a range of energy scales. The prospects for obtaining these conditions are studied by analyzing both the weak coupling and the intermediate coupling behavior, together with the connecting crossover region. Unfortunately, the conclusions are rather pessimistic. The phase diagram and the important crossover are analyzed via bosonization and refermionization and some of the results compared to those obtained from conformal field theory. Finally, an additional non-Fermi liquid fixed point is found, a multicritical point with two relevant directions even in the unbiased case.
It has been conjectured that an impurity with charge Z greater or equal to 2 can be localized due to its interaction with electrons in a metal. The simplest case is an impurity free to move between only two sites, which interacts locally with s-wave electrons. For Z greater or equal to 2 the hopping of the impurity is formally irrelevant and this has been argued to lead to localization. In this paper it is shown that other processes, in particular joint hopping of the impurity and one or more electrons between the sites, play an important role and have not been treated properly in the literature. Being relevant in a renormalization group sense, even when Z greater or equal to 2, these terms lead to delocalization of the impurity. Using bosonization, it is shown how these processes are generated from marginal operators that are usually neglected and the dangers of ignoring marginal or irrelevant operators are discussed in detail. Questions about implications for the more general situation of many sites to which the impurity can hop, are also considered.