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

Interaction of quasilocal harmonic modes and boson peak in glasses

The direct proportionality relation between the boson peak maximum in glasses, $\omega_b$, and the Ioffe-Regel crossover frequency for phonons, $\omega_d$, is established. For several investigated materials $\omega_b = (1.5\pm 0.1)\omega_d$. At the frequency $\omega_d$ the mean free path of the phonons $l$ becomes equal to their wavelength because of strong resonant scattering on quasilocal harmonic oscillators. Above this frequency phonons cease to exist. We prove that the established correlation between $\omega_b$ and $\omega_d$ holds in the general case and is a direct consequence of bilinear coupling of quasilocal oscillators with the strain field.Comment: RevTex, 4 pages, 1 figur

Observation of a New Surface State on 4He Crystal Interfaces

The equilibrium shape of hcp 4He crystals has been studied at temperatures 0.05≤T≤0.7 K by means of a high-precision optical interferometer. We find that the profile of the interfacial boundary, close to an almost horizontal c-facet, has a well-defined slope discontinuity separating two angular regions with different behavior of the surface stiffness α̃. For surfaces tilted by an angle φ≲100 μrad with respect to the c-facet, we obtain α̃=κ/φ, contrary to the linear angular dependence predicted by current theories. Our results on four large crystals yield κ=(11±3)×10 exp −4T erg/ cm exp 2 K.Peer reviewe

Facet Growth of 4He Crystals at mK Temperatures

We have investigated growth of c facets in good quality helium crystals with screw dislocation densities 0–20 cm exp −2 along the c axis. Three distinct regimes of growth were observed. One of them can be explained by spiral growth provided that kinetic energy of moving steps and their tendency to localization at large driving forces are taken into account. In the absence of screw dislocations we find burstlike growth unless the speed is less than 0.5 nm/s, in which case anomalous, intrinsic growth of facets is detected.Peer reviewe

Universal behavior of internal friction in glasses below T : anharmonicity vs relaxation

Comparison of the internal friction at hypersonic frequencies between a few K and the glass transition temperature Tg for various glasses brings out general features. At low temperature, internal friction is only weakly dependent on the material. At high temperature but still below Tg the internal friction for strong glasses shows a T-independent plateau in a very wide domain of temperature; in contrast, for fragile glass, a nearly linear variation of internal friction with T is observed. Anharmonicity appears dominant over thermally activated relaxational processes at high temperature.Comment: accepted in Physical Review

Equilibrium Low Temperature Heat Capacity of the Spin Density Wave compound (TMTTF)2 Br: effect of a Magnetic Field

We have investigated the effect of the magnetic field (B) on the very low-temperature equilibrium heat capacity ceq of the quasi-1 D organic compound (TMTTF)2Br, characterized by a commensurate Spin Density Wave (SDW) ground state. Below 1K, ceq is dominated by a Schottky-like contribution, very sensitive to the experimental time scale, a property that we have previously measured in numerous DW compounds. Under applied field (in the range 0.2- 7 T), the equilibrium dynamics, and hence ceq extracted from the time constant, increases enormously. For B = 2-3 T, ceq varies like B2, in agreement with a magnetic Zeeman coupling. Another specific property, common to other Charge/Spin density wave (DW) compounds, is the occurrence of metastable branches in ceq, induced at very low temperature by the field exceeding a critical value. These effects are discussed within a generalization to SDWs in a magnetic field of the available Larkin-Ovchinnikov local model of strong pinning. A limitation of the model when compared to experiments is pointed out.Comment: 10 pages, 11 figure

Studying damage accumulation in martensitic corrosion-resistant steel under cold radial reduction

Cold radial reduction of specimens made of the Kh17N2 corrosion-resistant martensitic steel is studied on a lever-type radial-forging machine (RFM). The mechanical properties of the deformed specimens, the "damage accumulation - strain" relation in the specimens are obtained with the application of hydrostatic and fractographic methods for fractured specimens. The damage of the Kh17N2 corrosion-resistant steel is evaluated as a result of an experimental study considering the data of simulation by a complex finite element model of cold deformation on a lever-type RFM. © 2017 Author(s)

Hypersound damping in vitreous silica measured by picosecond acoustics

The attenuation of longitudinal acoustic phonons up to frequencies nearing 250 GHz is measured in vitreous silica with a picosecond optical technique. Taking advantage of interferences on the probe beam, difficulties encountered in early pioneering experiments are alleviated. Sound damping at 250 GHz and room temperature is consistent with relaxation dominated by anharmonic interactions with the thermal bath, extending optical Brillouin scattering data. Our result is at variance with claims of a recent deep-UV experiment which reported a rapid damping increase beyond 100 GHz. A comprehensive picture of the frequency dependence of sound attenuation in $v$-SiO$_2$ can be proposed.Comment: 4 pages, 3 figure

Low temperature dipolar echo in amorphous dielectrics: Significance of relaxation and decoherence free two level systems

The nature of dielectric echoes in amorphous solids at low temperatures is investigated. It is shown that at long delay times the echo amplitude is determined by a small subset of two level systems (TLS) having negligible relaxation and decoherence because of their weak coupling to phonons. The echo decay can then be described approximately by power law time dependencies with different powers at times longer and shorter than the typical TLS relaxation time. The theory is applied to recent measurements of two and three pulse dipolar echo in borosilicate glass BK7 and provides a perfect data fit in the broad time and temperature ranges under the assumption that there exist two TLS relaxation mechanisms due to TLS-phonons and TLS-TLS interaction. This interpretation is consistent with the previous experimental and theoretical investigations. Further experiments verifying the theory predictions are suggested.Comment: 10 pages, 8 figure

Effect of Nuclear Quadrupole Interaction on the Relaxation in Amorphous Solids

Recently it has been experimentally demonstrated that certain glasses display an unexpected magnetic field dependence of the dielectric constant. In particular, the echo technique experiments have shown that the echo amplitude depends on the magnetic field. The analysis of these experiments results in the conclusion that the effect seems to be related to the nuclear degrees of freedom of tunneling systems. The interactions of a nuclear quadrupole electrical moment with the crystal field and of a nuclear magnetic moment with magnetic field transform the two-level tunneling systems inherent in amorphous dielectrics into many-level tunneling systems. The fact that these features show up at temperatures $T<100mK$, where the properties of amorphous materials are governed by the long-range $R^{-3}$ interaction between tunneling systems, suggests that this interaction is responsible for the magnetic field dependent relaxation. We have developed a theory of many-body relaxation in an ensemble of interacting many-level tunneling systems and show that the relaxation rate is controlled by the magnetic field. The results obtained correlate with the available experimental data. Our approach strongly supports the idea that the nuclear quadrupole interaction is just the key for understanding the unusual behavior of glasses in a magnetic field.Comment: 18 pages, 9 figure