Spectral responses in granular compaction

The slow compaction of a gently tapped granular packing is reminiscent of the low-temperature dynamics of structural and spin glasses. Here, I probe the dynamical spectrum of granular compaction by measuring a complex (frequency-dependent) volumetric susceptibility $\tilde{\chi}_v$. While the packing density $\rho$ displays glass-like slow relaxations (aging) and history-dependence (memory) at low tapping amplitudes, the susceptibility $\tilde{\chi}_v$ displays very weak aging effects, and its spectrum shows no sign of a rapidly growing timescale. These features place $\tilde{\chi}_v$ in sharp contrast to its dielectric and magnetic counterparts in structural and spin glasses; instead, $\tilde\chi_v$ bears close similarities to the complex specific heat of spin glasses. This, I suggest, indicates the glass-like dynamics in granular compaction are governed by statistically rare relaxation processes that become increasingly separated in timescale from the typical relaxations of the system. Finally, I examine the effect of finite system size on the spectrum of compaction dynamics. Starting from the ansatz that low frequency processes correspond to large scale particle rearrangements, I suggest the observed finite size effects are consistent with the suppression of large-scale collective rearrangements in small systems.Comment: 18 pages, 17 figures. Submitted to PR

Structural Order in Glassy Water

We investigate structural order in glassy water by performing classical molecular dynamics simulations using the extended simple point charge (SPC/E) model of water. We perform isochoric cooling simulations across the glass transition temperature at different cooling rates and densities. We quantify structural order by orientational and translational order metrics. Upon cooling the liquid into the glassy state, both the orientational order parameter $Q$ and translational order parameter $\tau$ increase. At T=0 K, the glasses fall on a line in the $Q$-$\tau$ plane or {\it order map}. The position of this line depends only on density and coincides with the location in the order map of the inherent structures (IS) sampled upon cooling. We evaluate the energy of the IS, $e_{IS}(T)$, and find that both order parameters for the IS are proportional to $e_{IS}$. We also study the structural order during the transformation of low-density amorphous ice (LDA) to high-density amorphous ice (HDA) upon isothermal compression and are able to identify distinct regions in the order map corresponding to these glasses. Comparison of the order parameters for LDA and HDA with those obtained upon isochoric cooling indicates major structural differences between glasses obtained by cooling and glasses obtained by compression. These structural differences are only weakly reflected in the pair correlation function. We also characterize the evolution of structural order upon isobaric annealing, leading at high pressure to very-high density amorphous ice (VHDA).Comment: submitte

Density of States for a Specified Correlation Function and the Energy Landscape

The degeneracy of two-phase disordered microstructures consistent with a specified correlation function is analyzed by mapping it to a ground-state degeneracy. We determine for the first time the associated density of states via a Monte Carlo algorithm. Our results are described in terms of the roughness of the energy landscape, defined on a hypercubic configuration space. The use of a Hamming distance in this space enables us to define a roughness metric, which is calculated from the correlation function alone and related quantitatively to the structural degeneracy. This relation is validated for a wide variety of disordered systems.Comment: Accepted for publication in Physical Review Letter

Electronic and phononic properties of cinnabar: ab initio calculations and some experimental results

We report ab initio calculations of the electronic band structure, the corresponding optical spectra, and the phonon dispersion relations of trigonal alpha-HgS (cinnabar). The calculated dielectric functions are compared with unpublished optical measurements by Zallen and coworkers. The phonon dispersion relations are used to calculate the temperature and isotopic mass dependence of the specific heat which has been compared with experimental data obtained on samples with the natural isotope abundances of the elements Hg and S (natural minerals and vapor phase grown samples) and on samples prepared from isotope enriched elements by vapor phase transport. Comparison of the calculated vibrational frequencies with Raman and ir data is also presented. Contrary to the case of cubic beta-HgS (metacinnabar), the spin-orbit splitting of the top valence bands at the Gamma-point of the Brillouin zone (Delta_0) is positive, because of a smaller admixture of 5d core electrons of Hg. Calculations of the lattice parameters, and the pressure dependence of Delta_0 and the corresponding direct gap E_0~2eV are also presented. The lowest absorption edge is confirmed to be indirect.Comment: 13 pages, 15 figure

Analytic solution of the fractional advection diffusion equation for the time-of-flight experiment in a finite geometry

A general analytic solution to the fractional advection diffusion equation is obtained in plane parallel geometry. The result is an infinite series of spatial Fourier modes which decay according to the Mittag-Leffler function, which is cast into a simple closed form expression in Laplace space using the Poisson summation theorem. An analytic expression for the current measured in a time-of-flight experiment is derived, and the sum of the slopes of the two respective time regimes on logarithmic axes is demonstrated to be -2, in agreement with the well known result for a continuous time random walk model. The sensitivity of current and particle number density to variation of experimentally controlled parameters is investigated in general, and the results applied to analyze selected experimental data.Comment: 10 pages, 6 figure

Phase Transitions in a Two-Component Site-Bond Percolation Model

A method to treat a N-component percolation model as effective one component model is presented by introducing a scaled control variable $p_{+}$. In Monte Carlo simulations on $16^{3}$, $32^{3}$, $64^{3}$ and $128^{3}$ simple cubic lattices the percolation threshold in terms of $p_{+}$ is determined for N=2. Phase transitions are reported in two limits for the bond existence probabilities $p_{=}$ and $p_{\neq}$. In the same limits, empirical formulas for the percolation threshold $p_{+}^{c}$ as function of one component-concentration, $f_{b}$, are proposed. In the limit $p_{=} = 0$ a new site percolation threshold, $f_{b}^{c} \simeq 0.145$, is reported.Comment: RevTeX, 5 pages, 5 eps-figure

Classical Spin Models with Broken Continuous Symmetry: Random Field Induced Order and Persistence of Spontaneous Magnetization

We consider a classical spin model, of two-dimensional spins, with continuous symmetry, and investigate the effect of a symmetry breaking unidirectional quenched disorder on the magnetization of the system. We work in the mean field regime. We show, by numerical simulations and by perturbative calculations in the low as well as in the high temperature limits, that although the continuous symmetry of the magnetization is lost, the system still magnetizes, albeit with a lower value as compared to the case without disorder. The critical temperature at which the system starts magnetizing, also decreases with the introduction of disorder. However, with the introduction of an additional constant magnetic field, the component of magnetization in the direction that is transverse to the disorder field increases with the introduction of the quenched disorder. We discuss the same effects also for three-dimensional spins.Comment: 12 pages, 12 figures, RevTeX

Topologically disordered systems at the glass transition

The thermodynamic approach to the viscosity and fragility of amorphous oxides was used to determine the topological characteristics of the disordered network-forming systems. Instead of the disordered system of atoms we considered the congruent disordered system of interconnecting bonds. The Gibbs free energy of network-breaking defects (configurons) was found based on available viscosity data. Amorphous silica and germania were used as reference disordered systems for which we found an excellent agreement of calculated and measured glass transition temperatures. We reveal that the Hausdorff dimension of the system of bonds changes from Euclidian three-dimensional below to fractal 2.55 ± 0.05-dimensional geometry above the glass transition temperature

Regular packings on periodic lattices

We investigate the problem of packing identical hard objects on regular lattices in d dimensions. Restricting configuration space to parallel alignment of the objects, we study the densest packing at a given aspect ratio X. For rectangles and ellipses on the square lattice as well as for biaxial ellipsoids on a simple cubic lattice, we calculate the maximum packing fraction \phi_d(X). It is proved to be continuous with an infinite number of singular points X^{\rm min}_\nu, X^{\rm max}_\nu, \nu=0, \pm 1, \pm 2,... In two dimensions, all maxima have the same height, whereas there is a unique global maximum for the case of ellipsoids. The form of \phi_d(X) is discussed in the context of geometrical frustration effects, transitions in the contact numbers and number theoretical properties. Implications and generalizations for more general packing problems are outlined.Comment: 5 pages, 4 figures, accepted for publication in Physical Review Letter

Multi-Gap Superconductivity in MgB2: Magneto-Raman Spectroscopy

Electronic Raman scattering studies on MgB2 single crystals as a function of excitation and polarization have revealed three distinct superconducting features: a clean gap below 37 cm-1 and two coherence peaks at 109 cm-1 and 78 cm-1 which we identify as the superconducting gaps in \pi- and \sigma-bands and as the Leggett's collective mode arising from the fluctuation in the relative phase between two superconducting condensates residing on corresponding bands. The temperature and field dependencies of the superconducting features have been established. A phononic Raman scattering study of the E2g boron stretching mode anharmonicity and of superconductivity induced self-energy effects is presented. We show that anharmonic two phonon decay is mainly responsible for the unusually large linewidth of the E2g mode. We observe ~2.5% hardening of the E2g phonon frequency upon cooling into the superconducting state and estimate the electron-phonon coupling strength associated with this renormalization.Comment: Invited review in a special issue "Superconductivity in MgB_2: Physics and Applications