Low-temperature specific heat of real crystals: Possibility of leading contribution of optical and short-wavelength acoustical vibrations

We point out that the repeatedly reported glass-like properties of crystalline materials are not necessarily associated with localized (or quasilocalized) excitations. In real crystals, optical and short-wavelength acoustical vibrations remain damped due to defects down to zero temperature. If such a damping is frequency-independent, e.g. due to planar defects or charged defects, these optical and short-wavelength acoustical vibrations yield a linear-in-$T$ contribution to the low-temperature specific heat of the crystal lattices. At low enough temperatures such a contribution will prevail over that of the long-wavelength acoustical vibrations (Debye contribution). The crossover between the linear and the Debye regime takes place at $T^* \propto \sqrt N$, where $N$ is the concentration of the defects responsible for the damping. Estimates show that this crossover could be observable.Comment: 5 pages. v4: Error in Appendix corrected, which does not change the main results of the pape

Algebraic theories of brackets and related (co)homologies

A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to geometry.Comment: 14 pages; v2: minor correction

Pion Energy Reconstruction by the Local Hadronic Calibration Method with ATLAS Combined Test Beam 2004 data

The pion energy reconstruction by the local hadronic calibration method on the basis of the 2004 combined test beam data in the energy range 10 -- 350 GeV and $\eta = 0.25$ is performed. In this method energies deposited in each cell are weighted. The weights are determined by the Monte Carlo simulation using Calibration Hits software. We have modified this method by applying cuts in weights. The obtained fractional energy resolution with the conventional method of determination of the energy deposit in the dead material between LAr and Tile calorimeters is $\sigma/E = (67\pm2)\%/\sqrt{E} \oplus (3.9\pm0.2)\% \oplus (95\pm22)\%/E$. This is about 1.5 times better than the results for the hadronic calibration method obtained by the Oxford-Stockholm group and slightly better than the H1 method results for CTB04 obtained by Pisa group. The energy linearity is within $\pm$1\%. We have determined the general normalization constant of 0.91 for which the mean value linearity for the weight cut of 1.05 is about 1. At using this normalization constant the energy resolution has not worsen. We have corrected the cesium miscalibration of the $Tile_1$ and $Tile_2$ longitudinal samplings. The mean value of energy linearity has been increased by about 1\% and becomes equal to 1.002$\pm$0.002. The energy resolution did not change. We have performed weighting without knowing of the beam energies. For this the special procedure has been developed. In this case the energy resolution shows 9\% degradation. Linearities are within $\pm$1\%. We have applied the Neural Networks to the determination of the energy deposit between LAr and Tile calorimeters. The essential improvement of energy resolution is obtained. In this case we have reached the projected energy resolution for hadrons in the ATLAS detector $\sigma/E = 50\%/\sqrt{E} \oplus 3\%$

Electromagnetic wave refraction at an interface of a double wire medium

Plane-wave reflection and refraction at an interface with a double wire medium is considered. The problem of additional boundary conditions (ABC) in application to wire media is discussed and an ABC-free approach, known in the solid state physics, is used. Expressions for the fields and Poynting vectors of the refracted waves are derived. Directions and values of the power density flow of the refracted waves are found and the conservation of the power flow through the interface is checked. The difference between the results, given by the conventional model of wire media and the model, properly taking into account spatial dispersion, is discussed.Comment: 17 pages, 11 figure