Two-parametric deformation Up,q[gl(2/1)]U_{p,q}[gl(2/1)] and its induced representations

The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical) finite-dimensional representations of this quantum superalgebra. In spite of some specific features, the present approach is similar to a previously developed method [1] which, as shown here, is applicable not only to the one-parametric quantum deformations but also to the multi-parametric ones.Comment: Latex, 13 pages, no figur

What is the right theory for Anderson localization of light?

Anderson localization of light is traditionally described in analogy to electrons in a random potential. Within this description the disorder strength -- and hence the localization characteristics -- depends strongly on the wavelength of the incident light. In an alternative description in analogy to sound waves in a material with spatially fluctuating elastic moduli this is not the case. Here, we report on an experimentum crucis in order to investigate the validity of the two conflicting theories using transverse-localized optical devices. We do not find any dependence of the observed localization radii on the light wavelength. We conclude that the modulus-type description is the correct one and not the potential-type one. We corroborate this by showing that in the derivation of the traditional, potential-type theory a term in the wave equation has been tacititly neglected. In our new modulus-type theory the wave equation is exact. We check the consistency of the new theory with our data using a field-theoretical approach (nonlinear sigma model)

Localization-delocalization transition for disordered cubic harmonic lattices

We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams exhibit regions of stable and unstable waves, the universality of the transitions is the same for mass and spring constant disorder throughout all the phase boundaries. The combined value for the critical exponent of the localization lengths of $\nu = 1.550^{+0.020}_{-0.017}$ confirms the agreement with the universality class of the standard electronic Anderson model of localization. We further support our investigation with studies of the density of states, the participation numbers and wave function statistics.Comment: 12 pages, 8 figures, 1 tabl

Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states

The evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wave length and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wave length with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by X-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.Comment: 50 pages, 17 postscript files including 18 figures, to be published in Phys. Rev.

Density of states in random lattices with translational invariance

We propose a random matrix approach to describe vibrational excitations in disordered systems. The dynamical matrix M is taken in the form M=AA^T where A is some real (not generally symmetric) random matrix. It guaranties that M is a positive definite matrix which is necessary for mechanical stability of the system. We built matrix A on a simple cubic lattice with translational invariance and interaction between nearest neighbors. We found that for certain type of disorder phonons cannot propagate through the lattice and the density of states g(w) is a constant at small w. The reason is a breakdown of affine assumptions and inapplicability of the elasticity theory. Young modulus goes to zero in the thermodynamic limit. It strongly reminds of the properties of a granular matter at the jamming transition point. Most of the vibrations are delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil. Mag. B v.79, 1715 (1999).Comment: 4 pages, 5 figure

On the high-density expansion for Euclidean Random Matrices

Diagrammatic techniques to compute perturbatively the spectral properties of Euclidean Random Matrices in the high-density regime are introduced and discussed in detail. Such techniques are developed in two alternative and very different formulations of the mathematical problem and are shown to give identical results up to second order in the perturbative expansion. One method, based on writing the so-called resolvent function as a Taylor series, allows to group the diagrams in a small number of topological classes, providing a simple way to determine the infrared (small momenta) behavior of the theory up to third order, which is of interest for the comparison with experiments. The other method, which reformulates the problem as a field theory, can instead be used to study the infrared behaviour at any perturbative order.Comment: 29 page

Localized and Delocalized Charge Transport in Single-Wall Carbon-Nanotube Mats

We measured the complex dielectric constant in mats of single-wall carbon-nanotubes between 2.7 K and 300 K up to 0.5 THz. The data are well understood in a Drude approach with a negligible temperature dependence of the plasma frequency (omega_p) and scattering time (tau) with an additional contribution of localized charges. The dielectric properties resemble those of the best ''metallic'' polypyrroles and polyanilines. The absence of metallic islands makes the mats a relevant piece in the puzzle of the interpretation of tau and omega_p in these polymers.Comment: 4 pages including 4 figure

Inelastic light, neutron, and X-ray scatterings related to the heterogeneous elasticity of glasses

The effects of plasticization of poly(methyl methacrylate) glass on the boson peaks observed by Raman and neutron scattering are compared. In plasticized glass the cohesion heterogeneities are responsible for the neutron boson peak and partially for the Raman one, which is enhanced by the composition heterogeneities. Because the composition heterogeneities have a size similar to that of the cohesion ones and form quasiperiodic clusters, as observed by small angle X-ray scattering, it is inferred that the cohesion heterogeneities in a normal glass form nearly periodic arrangements too. Such structure at the nanometric scale explains the linear dispersion of the vibrational frequency versus the transfer momentum observed by inelastic X-ray scattering.Comment: 9 pages, 2 figures, to be published in J. Non-Cryst. Solids (Proceedings of the 4th IDMRCS