Finite linear groups, lattices, and products of elliptic curves

Let $V$ be a finite dimensional complex linear space and let $G$ be an irreducible finite subgroup of \GL(V). For a $G$-invariant lattice $\Lambda$ in $V$ of maximal rank, we give a description of structure of the complex torus $V/\Lambda$. In particular, we prove that for a wide class of groups, $V/\Lambda$ is isogenous to a self-product of an elliptic curve, and that in many cases $V/\Lambda$ is isomorphic to a product of mutually isogenous elliptic curves with complex multiplication. We show that there are $G$ and $\Lambda$ such that the complex torus $V/\Lambda$ is not an abelian variety but one can always replace $\Lambda$ by another $G$-invariant lattice $\Delta$ such that $V/\Delta$ is a product if elliptic curves with complex multiplication. We amplify these results with a criterion, in terms of the character and the Schur $\mathbf Q$-index of $G$-module $V$, of the existence of a nonzero $G$-invariant lattice in $V$.Comment: 25 pages. Several examples are adde

The experimental study of the surface current excitation under the influence of a relativistic electron electromagnetic field

The problem of the surface current excitation in a conductive targets by a relativistic electron electric field as the origin of such radiation mechanisms as diffraction and transition radiation of relativistic electron was considered in frame of both surface current and pseudo-photon methods. The contradiction between these viewpoints in respect to the surface current on the target downstream surface necessitated the experimental test of this phenomenon. The test performed on electron beam of the 6 MeV microtron showed, that not any surface current is induced on the target downstream surface under the influence of a relativistic electron electromagnetic field in contrast to the upstream surface. This is important implication for the understanding of the forward transition and diffraction radiation nature.Comment: Was Presented at the symposium Channeling 2008 (Charged and Neutral Particles Channeling Phenomena), October 25 - November 1, 2008 Erice (Trapani - Sicily), Italy, and was accepted for publication in proceedings of symposiu

Parametric study of the conditions of supershear crack propagation in brittle materials

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in AIP Conference Proceedings 1683, 020209 (2015) and may be found at https://doi.org/10.1063/1.4932899.The paper is devoted to the numerical analysis of the conditions of acceleration of dynamically propagating longitudinal shear cracks from sub-Rayleigh to intersonic/supershear velocities. We showed that an ability of the initial crack to propagate in supershear regime can be predicted with use of the empirically derived dependence of the geometrical criterion of sub-Raleigh-to-intersonic transition on material and crack parameters

Schwinger Pair Creation of Particles and Strings

I shortly review the worldline instanton method for calculating Schwinger pair production rates in (i) one-loop QED (ii) multiloop QED and (iii) one-loop open string theory.Comment: 8 pages, 3 figures, talk given at XIV Mexican School of Particles and Fields, November 8 - 12, 2010, Morelia, Mexico, to appear in the conference proceeding

Thermodynamic Properties of Kagome Lattice in ZnCu_3(OH)_6Cl_2 Herbertsmithite

Strongly correlated Fermi systems are among the most intriguing and fundamental systems in physics, whose realization in some compounds is still to be discovered. We show that herbertsmithite ZnCu_3(OH)_6Cl_2 can be viewed as a strongly correlated Fermi system whose low temperature thermodynamic in magnetic fields is defined by a quantum critical spin liquid. Our calculations of its thermodynamic properties are in good agreement with recent experimental facts and allow us to reveal their scaling behavior which strongly resembles that observed in HF metals and 2D 3He.Comment: 4 pages, 6 figure

A young contracting white dwarf in the peculiar binary HD 49798/RX J0648.0--4418?

HD 49798/RX J0648.0--4418 is a peculiar X-ray binary with a hot subdwarf (sdO) mass donor. The nature of the accreting compact object is not known, but its spin period $P=13.2$~s and $\dot P =-2.15 \times 10^{-15}$s~s$^{-1}$, prove that it can be only either a white dwarf or a neutron star. The spin-up has been very stable for more than 20 years. We demonstrate that the continuous stable spin-up of the compact companion of HD 49798 can be best explained by contraction of a young white dwarf with an age $\sim 2$~Myrs. This allows us to interpret all the basic parameters of the system in the framework of an accreting white dwarf. We present examples of binary evolution which result in such systems. If correct, this is the first direct evidence for a white dwarf contraction on early evolutionary stages.Comment: 9 pages, accepted to MNRA