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

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

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