Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements

We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as generalizations of complete sets of mutually unbiased bases, being equivalent whenever the design is composed of d+1 bases in dimension d. We show that, for the purpose of quantum state determination, these designs specify an optimal collection of orthogonal measurements. Using highly nonlinear functions on abelian groups, we construct explicit examples from d+2 orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10, and 12, for example, where no complete sets of mutually unbiased bases have thus far been found.Comment: 28 pages, to appear in J. Math. Phy

Fukushima plutonium effect and blow-up regimes in neutron-multiplying media

It is shown that the capture and fission cross-sections of 238U and 239Pu increase with temperature within 1000-3000 K range, in contrast to those of 235U, that under certain conditions may lead to the so-called blow-up modes, stimulating the anomalous neutron flux and nuclear fuel temperature growth. Some features of the blow-up regimes in neutron-multiplying media are discussed.Comment: 15 pages, 8 figures. (v2: numerous corrections and style improvements). arXiv admin note: substantial text overlap with arXiv:1207.369

Resonance-like piezoelectric electron-phonon interaction in layered structures

We show that mismatch of the piezoelectric parameters between layers of multiple-quantum well structures leads to modification of the electron-phonon interaction. In particular, short-wavelength phonons propagating perpendicular to the layers with wavevector close to $2\pi n/d$, where $d$ is the period of the structure, induce a strong smoothly-varying component of the piezo-potential. As a result, they interact efficiently with 2D electrons. It is shown, that this property leads to emission of collimated quasi-monochromatic beams of high-frequency acoustic phonons from hot electrons in multiple-quantum well structures. We argue that this effect is responsible for the recently reported monochromatic transverse phonon emission from optically excited GaAs/AlAs superlattices, and provide additional experimental evidences of this.Comment: 6 pages, 7 figure

Mechanism of Deep-focus Earthquakes Anomalous Statistics

Analyzing the NEIC-data we have shown that the spatial deep-focus earthquake distribution in the Earth interior over the 1993-2006 is characterized by the clearly defined periodical fine discrete structure with period L=50 km, which is solely generated by earthquakes with magnitude M 3.9 to 5.3 and only on the convergent boundary of plates. To describe the formation of this structure we used the model of complex systems by A. Volynskii and S. Bazhenov. The key property of this model consists in the presence of a rigid coating on a soft substratum. It is shown that in subduction processes the role of a rigid coating plays the slab substance (lithosphere) and the upper mantle acts as a soft substratum. Within the framework of this model we have obtained the estimation of average values of stress in the upper mantle and Young's modulus for the oceanic slab (lithosphere) and upper mantle.Comment: 9 pages, 7 figure