On consistency of hydrodynamic approximation for chiral media

We consider chiral liquids, that is liquids consisting of massless fermions and right-left asymmetric. In such media, one expects existence of electromagnetic current flowing along an external magnetic field, associated with the chiral anomaly. The current is predicted to be dissipation-free. We consider dynamics of chiral liquids, concentrating on the issues of possible instabilities and infrared sensitivity. Instabilities arise, generally speaking, already in the limit of vanishing electromagnetic constant, $\alpha_{el}\to 0$. In particular, liquids with non-vanishing chiral chemical potential might decay into right-left asymmetric states containing vortices.Comment: Published versio

Chiral Vortical Effect in Superfluid

We consider rotating superfluid pionic liquid, with superfluidity being induced by isospin chemical potential. The rotation is known to result in a chiral current flowing along the axis of the rotation. We argue that in case of superfluidity the chiral current is realized on fermionic zero modes propagating along vortices. The current evaluated in this way differs by a factor of two from the standard one. The reason is that the chiral charge is carried by zero modes which propagate with speed of light, and thus the liquid cannot be described by a single (local) velocity, like it is assumed in standard derivations.Comment: 10 pages. To be published in PRD. Minor changes added; typos fixe

Coulomb corrections to the Delbrueck scattering amplitude at low energies

In this article, we study the Coulomb corrections to the Delbrueck scattering amplitude. We consider the limit when the energy of the photon is much less than the electron mass. The calculations are carried out in the coordinate representation using the exact relativistic Green function of an electron in a Coulomb field. The resulting relative corrections are of the order of a few percent for scattering on for a large charge of the nucleus. We compare the corrections with the corresponding ones calculated through the dispersion integral of the pair production cross section and also with the magnetic loop contribution to the g-factor of a bound electron. The last one is in a good agreement with our results but the corrections calculated through the dispersion relation are not.Comment: 8 pages, 6 figure

Research of ways of realization of the information interchange controller for the specialized computing module and implementation variation choice

Рассмотрена задача реализации контроллера системной магистрали для вычислительного модуля, предназначенного для использования в составе цифровой вычислительной системы семейства «Малахит». Контроллер выполнен на базе программируемой логической интегральной схемы и осуществляет сопряжение процессора серии «Мультикор», являющегося ядром модуля, с системной магистралью. Проработаны варианты реализации контроллера для конкретной приборной реализации модуля, сделаны выводы и рекомендации по их применению.The problem of implementation of the information interchange controller that is intended for the specialized computing system is discussed. The controller is implemented on programmable logic integrated circuits and provides processor of series «multicore» and information interchange interface logical connective. The ways of controller realization are researched and recommendations of efficient controller variations use are made

Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU

The NP-hard Multiple Hitting Set problem is finding a minimum-cardinality set intersecting each of the sets in a given input collection a given number of times. Generalizing a well-known data reduction algorithm due to Weihe, we show a problem kernel for Multiple Hitting Set parameterized by the Dilworth number, a graph parameter introduced by Foldes and Hammer in 1978 yet seemingly so far unexplored in the context of parameterized complexity theory. Using matrix multiplication, we speed up the algorithm to quadratic sequential time and logarithmic parallel time. We experimentally evaluate our algorithms. By implementing our algorithm on GPUs, we show the feasability of realizing kernelization algorithms on SIMD (Single Instruction, Multiple Date) architectures.Comment: Added experiments on one more data se