Effect of a Magnetic Field on the Dipole Echo in Glasses with Nuclear Quadrupole Moments

The effect of a magnetic field on the dipole echo amplitude in glasses at temperatures of about 10 mK caused by nonspherical nuclei with electric quadrupole moments has been studied theoretically. It has been shown that in this case, the two-level systems (TLS's) that determine the glass properties at low temperatures are transformed into more complicated multilevel systems. These systems have new properties as compared to usual TLS's and, in particular, exhibit oscillations of electric dipole echo amplitude in magnetic field. A general formula that describes the echo amplitude in an arbitrary split TLS has been derived with perturbation theory. Detailed analytic and numerical analysis of the formula has been performed. The theory agrees qualitatively and quantitatively well with experimental data.Comment: 5 pages, 3 figure

Oscillations of Echo Amplitude in Glasses in a Magnetic Field Induced by Nuclear Dipole-Dipole Interaction

The effect of a magnetic field on the dipole echo amplitude in glasses (at temperatures of about 10 mK) induced by the dipole-dipole interaction of nuclear spins has been theoretically studied. It has been shown that a change in the positions of nuclear spins as a result of tunneling and their interaction with the external magnetic field E_H lead to a nonmonotonic magnetic field dependence of the dipole echo amplitude. The approximation that the nuclear dipole-dipole interaction energy E_d is much smaller than the Zeeman energy E_H has been found to be valid in the experimentally important cases. It has been shown that the dipole echo amplitude in this approximation may be described by a simple universal analytic function independent of the microscopic structure of the two-level systems. An excellent agreement of the theory with the experimental data has been obtained without fitting parameters (except for the unknown echo amplitude)Comment: 5 pages, 1 figur

Harmonic analysis on local fields and adelic spaces II

This paper is the second part of arXiv:0707.1766. We develope harmonic analysis in some categories of filtered abelian groups and vector spaces over the fields R or C. These categories contain as objects local fields and adelic spaces arising from arithmetical surfaces. Some structure theorems are proven for quotients of the adelic groups of algebraic and arithmetical surfaces.Comment: 78 pages; corrected misprints; to appear in Izvestiya: Mathematic

Harmonic analysis and the Riemann-Roch theorem

This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from these papers and two-dimensional adelic theory we obtain the Riemann-Roch formula on a projective smooth algebraic surface over a finite field.Comment: 7 pages; to appear in Doklady Mathematic

Harmonic analysis on local fields and adelic spaces I

We develop a harmonic analysis on objects of some category $C_2$ of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. The main result is the theory of the Fourier transform on these objects and two-dimensional Poisson formulas.Comment: 69 pages; corrected typos and inserted some changes into the last sectio

Transverse and longitudinal vibrations in amorphous silicon

We show that harmonic vibrations in amorphous silicon can be decomposed to transverse and longitudinal components in all frequency range even in the absence of the well defined wave vector ${\bf q}$. For this purpose we define the transverse component of the eigenvector with given $\omega$ as a component, which does not change the volumes of Voronoi cells around atoms. The longitudinal component is the remaining orthogonal component. We have found the longitudinal and transverse components of the vibrational density of states for numerical model of amorphous silicon. The vibrations are mostly transverse below 7 THz and above 15 THz. In the frequency interval in between the vibrations have a longitudinal nature. Just this sudden transformation of vibrations at 7 THz from almost transverse to almost longitudinal ones explains the prominent peak in the diffusivity of the amorphous silicon just above 7 THz.Comment: 6 pages, 3 figure