Vibrational instability, two-level systems and Boson peak in glasses

We show that the same physical mechanism is fundamental for two seemingly different phenomena such as the formation of two-level systems in glasses and the Boson peak in the reduced density of low-frequency vibrational states g(w)/w^2. This mechanism is the vibrational instability of weakly interacting harmonic modes. Below some frequency w_c << w_0 (where w_0 is of the order of Debye frequency) the instability, controlled by the anharmonicity, creates a new stable universal spectrum of harmonic vibrations with a Boson peak feature as well as double-well potentials with a wide distribution of barrier heights. Both are determined by the strength of the interaction I ~ w_c between the oscillators. Our theory predicts in a natural way a small value for the important dimensionless parameter C ~ 10^{-4} for two-level systems in glasses. We show that C ~ I^{-3} and decreases with increasing of the interaction strength I. We show that the number of active two-level systems is very small, less than one per ten million of oscillators, in a good agreement with experiment. Within the unified approach developed in the present paper the density of the tunneling states and the density of vibrational states at the Boson peak frequency are interrelated.Comment: 28 pages, 3 figure

Some generic aspects of bosonic excitations in disordered systems

We consider non-interacting bosonic excitations in disordered systems, emphasising generic features of quadratic Hamiltonians in the absence of Goldstone modes. We discuss relationships between such Hamiltonians and the symmetry classes established for fermionic systems. We examine the density \rho(\omega) of excitation frequencies \omega, showing how the universal behavior \rho(\omega) ~ \omega^4 for small \omega can be obtained both from general arguments and by detailed calculations for one-dimensional models

Asymptotics of Eigenvalues and Eigenfunctions for the Laplace Operator in a Domain with Oscillating Boundary. Multiple Eigenvalue Case

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics

Current Assisted, Thermally Activated Flux Liberation in Ultrathin Nanopatterned NbN Superconducting Meander Structures

We present results from an extensive study of fluctuation phenomena in superconducting nanowires made from sputtered NbN. Nanoscale wires were fabricated in form of a meander and operated at a constant temperature T~0.4Tc(0). The superconducting state is driven close to the electronic phase transition by a high bias current near the critical one. Fluctuations of sufficient strength temporarily drive a section of the meander structure into the normal conducting state, which can be registered as a voltage pulse of nanosecond duration. We considered three different models (vortex-antivortex pairs, vortex edge barriers and phase slip centers) to explain the experimental data. Only thermally excited vortices, either via unbinding of vortex-antivortex pairs or vortices overcoming the edge barrier, lead to a satisfactory and consistent description for all measurements.Comment: 41 Pages, 5 Chapters, 7 Figures, 2 Tables, 30 Equations, 68 References; Selected for the January 15, 2010 Issue of the Virtual Journal of Applications of Superconductivit

Generation of small-scale structures in the developed turbulence

The Navier-Stokes equation for incompressible liquid is considered in the limit of infinitely large Reynolds number. It is assumed that the flow instability leads to generation of steady-state large-scale pulsations. The excitation and evolution of the small-scale turbulence is investigated. It is shown that the developed small-scale pulsations are intermittent. The maximal amplitude of the vorticity fluctuations is reached along the vortex filaments. Basing on the obtained solution, the pair correlation function in the limit $r\to 0$ is calculated. It is shown that the function obeys the Kolmogorov law $r^{2/3}$.Comment: 18 page

Hard loss of stability in Painlev\'e-2 equation

A special asymptotic solution of the Painlev\'e-2 equation with small parameter is studied. This solution has a critical point $t_*$ corresponding to a bifurcation phenomenon. When $t<t_*$ the constructed solution varies slowly and when $t>t_*$ the solution oscillates very fast. We investigate the transitional layer in detail and obtain a smooth asymptotic solution, using a sequence of scaling and matching procedures

Low-temperature specific heat and thermal conductivity of glycerol

We have measured the thermal conductivity of glassy glycerol between 1.5 K and 100 K, as well as the specific heat of both glassy and crystalline phases of glycerol between 0.5 K and 25 K. We discuss both low-temperature properties of this typical molecular glass in terms of the soft-potential model. Our finding of an excellent agreement between its predictions and experimental data for these two independent measurements constitutes a robust proof of the capabilities of the soft-potential model to account for the low-temperature properties of glasses in a wide temperature range.Comment: 4 pages, 3 figures. To be published in Phys. Rev. B (2002

The Vega Debris Disk -- A Surprise from Spitzer

We present high spatial resolution mid- and far-infrared images of the Vega debris disk obtained with the Multiband Imaging Photometer for Spitzer (MIPS). The disk is well resolved and its angular size is much larger than found previously. The radius of the disk is at least 43" (330 AU), 70"(543 AU), and 105" (815 AU) in extent at 24, 70 and 160 um, respectively. The disk images are circular, smooth and without clumpiness at all three wavelengths. The radial surface brightness profiles imply an inner boundary at a radius of 11"+/-2" (86 AU). Assuming an amalgam of amorphous silicate and carbonaceous grains, the disk can be modeled as an axially symmetric and geometrically thin disk, viewed face-on, with the surface particle number density following an r^-1 power law. The disk radiometric properties are consistent with a range of models using grains of sizes ~1 to ~50 um. We find that a ring, containing grains larger than 180 um and at radii of 86-200 AU from the star, can reproduce the observed 850 um flux, while its emission does not violate the observed MIPS profiles. This ring could be associated with a population of larger asteroidal bodies analogous to our own Kuiper Belt. Cascades of collisions starting with encounters amongthese large bodies in the ring produce the small debris that is blown outward by radiation pressure to much larger distances where we detect its thermal emission. The dust production rate is >~10^15 g/s based on the MIPS results. This rate would require a very massive asteroidal reservoir for the dust to be produced in a steady state throughout Vega's life. Instead, we suggest that the disk we imaged is ephemeral and that we are witnessing the aftermath of a large and relatively recent collisional event, and subsequent collisional cascade.Comment: 13 pages, 17 figures, accepted for publication in ApJ. (Figures 2, 3a, 3b and 4 have been degraded to lower resolutions.

Anharmonicity, vibrational instability and Boson peak in glasses

We show that a {\em vibrational instability} of the spectrum of weakly interacting quasi-local harmonic modes creates the maximum in the inelastic scattering intensity in glasses, the Boson peak. The instability, limited by anharmonicity, causes a complete reconstruction of the vibrational density of states (DOS) below some frequency $\omega_c$, proportional to the strength of interaction. The DOS of the new {\em harmonic modes} is independent of the actual value of the anharmonicity. It is a universal function of frequency depending on a single parameter -- the Boson peak frequency, $\omega_b$ which is a function of interaction strength. The excess of the DOS over the Debye value is $\propto\omega^4$ at low frequencies and linear in $\omega$ in the interval $\omega_b \ll \omega \ll \omega_c$. Our results are in an excellent agreement with recent experimental studies.Comment: LaTeX, 8 pages, 6 figure

Quantum interference of electrons in Nb_{5-\delta}Te_4 single crystals

The compound $Nb_{5-\delta}Te_4$ ($\delta=0.23$) with quasi-one-dimensional crystal structure undergoes a transition to superconductivity at $T_c$=0.6--0.9 K. Its electronic transport properties in the normal state are studied in the temperature range 1.3--270 K and in magnetic fields up to 11 T. The temperature variation of the resistivity is weak ($<2$) in the investigated temperature range. Nonmonotonic behavior of the resistivity is observed which is characterized by two local maxima at $T\sim$2 K and $\sim$30 K. The temperature dependence of the resistivity is interpreted as an interplay of weak localization, weak antilocalization, and electron-electron interaction effects in the diffusion and the Cooper channel. The temperature dependence of the dephasing time $\tau_\phi$ extracted from the magnetoresistance data is determined by the electron-phonon interaction. The saturation of $\tau_\phi$ in the low-temperature limit correlates with $T_c$ of the individual crystal and is ascribed to the scattering on magnetic impurities.Comment: 8 pages, 6 figure