Constructions of complex Hadamard matrices via tiling Abelian groups

Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling Abelian groups and constructions of complex Hadamard matrices. First, we recover a recent very general construction of complex Hadamard matrices due to Dita via a natural tiling construction. Then we find some necessary conditions for any given complex Hadamard matrix to be equivalent to a Dita-type matrix. Finally, using another tiling construction, due to Szabo, we arrive at new parametric families of complex Hadamard matrices of order 8, 12 and 16, and we use our necessary conditions to prove that these families do not arise with Dita's construction. These new families complement the recent catalogue of complex Hadamard matrices of small order.Comment: 15 page

Ab-initio elastic tensor of cubic Ti0.5_{0.5}Al0.5_{0.5}N alloy: the dependence of the elastic constants on the size and shape of the supercell model

In this study we discuss the performance of approximate SQS supercell models in describing the cubic elastic properties of B1 (rocksalt) Ti$_{0.5}$Al$_{0.5}$N alloy by using a symmetry based projection technique. We show on the example of Ti$_{0.5}$Al$_{0.5}$N alloy, that this projection technique can be used to align the differently shaped and sized SQS structures for a comparison in modeling elasticity. Moreover, we focus to accurately determine the cubic elastic constants and Zener's type elastic anisotropy of Ti$_{0.5}$Al$_{0.5}$N. Our best supercell model, that captures accurately both the randomness and cubic elastic symmetry, results in $C_{11}=447$ GPa, $C_{12}=158$ GPa and $C_{44}=203$ GPa with 3% of error and $A=1.40$ for Zener's elastic anisotropy with 6% of error. In addition, we establish the general importance of selecting proper approximate SQS supercells with symmetry arguments to reliably model elasticity of alloys. In general, we suggest the calculation of nine elastic tensor elements - $C_{11}$, $C_{22}$, $C_{33}$, $C_{12}$, $C_{13}$, $C_{23}$, $C_{44}$, $C_{55}$ and $C_{66}$, to evaluate and analyze the performance of SQS supercells in predicting elasticity of cubic alloys via projecting out the closest cubic approximate of the elastic tensor. The here described methodology is general enough to be applied in discussing elasticity of substitutional alloys with any symmetry and at arbitrary composition.Comment: Submitted to Physical Review

New fixed point action for SU(3) lattice gauge theory

We present a new fixed point action for SU(3) lattice gauge theory, which has --- compared to earlier published fixed point actions --- shorter interaction range and smaller violations of rotational symmetry in the static q\bar{q}-potential even at shortest distances

Crackling noise in three-point bending of heterogeneous materials

We study the crackling noise emerging during single crack propagation in a specimen under three-point bending conditions. Computer simulations are carried out in the framework of a discrete element model where the specimen is discretized in terms of convex polygons and cohesive elements are represented by beams. Computer simulations revealed that fracture proceeds in bursts whose size and waiting time distributions have a power law functional form with an exponential cutoff. Controlling the degree of brittleness of the sample by the amount of disorder, we obtain a scaling form for the characteristic quantities of crackling noise of quasi-brittle materials. Analyzing the spatial structure of damage we show that ahead of the crack tip a process zone is formed as a random sequence of broken and intact mesoscopic elements. We characterize the statistics of the shrinking and expanding steps of the process zone and determine the damage profile in the vicinity of the crack tip.Comment: 11 pages, 15 figure

Universal temperature dependence of optical excitation life-time and band-gap in chirality assigned semiconducting single-wall carbon nanotubes

The temperature dependence of optical excitation life-time, Gamma, and transition energies, E_ii, were measured for bucky-papers of single-wall carbon nanotubes (SWCNTs) and inner tubes in double-wall carbon nanotubes (DWCNTs) using resonant Raman scattering. The temperature dependence of Gamma and E_ii is the same for both types of samples and is independent of tube chirality. The data proves that electron-phonon interaction is responsible for temperature dependence of E_ii(T). The temperature independent inhomogeneous contribution to Gamma is much larger in the SWCNT samples, which is explained by the different SWCNT environment in the two types of samples. Gamma of the inner tubes for the bucky-paper DWCNT sample is as low as \sim 30 meV, which is comparable to that found for individual SWCNTs