Majorana fermions in pinned vortices

Exploiting the peculiar properties of proximity-induced superconductivity on the surface of a topological insulator, we propose a device which allows the creation of a Majorana fermion inside the core of a pinned Abrikosov vortex. The relevant Bogolyubov-de Gennes equations are studied analytically. We demonstrate that in this system the zero-energy Majorana fermion state is separated by a large energy gap, of the order of the zero-temperature superconducting gap $\Delta$, from a band of single-particle non-topological excitations. In other words, the Majorana fermion remains robust against thermal fluctuations, as long as the temperature remains substantially lower than the critical superconducting temperature. Experimentally, the Majorana state may be detected by measuring the tunneling differential conductance at the center of the Abrikosov vortex. In such an experiment, the Majorana state manifests itself as a zero-bias anomaly separated by a gap, of the order of $\Delta$, from the contributions of the nontopological excitations.Comment: 9 pages, 2 eps figures, new references are added, several typos are correcte

Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity

Using bosonization-fermionization transformation we map the Tomonaga-Luttinger model of spinless fermions with non-linear dispersion on the model of fermionic quasiparticles whose interaction is irrelevant in the renormalization group sense. Such mapping allows us to set up an expansion for the density-density propagator of the original Tomonaga-Luttinger Hamiltonian in orders of the (irrelevant) quasiparticle interaction. The lowest order term in such an expansion is proportional to the propagator for free fermions. The next term is also evaluated. The propagator found is used for calculation of the Coulomb drug resistivity $r$ in a system of two capacitively coupled one-dimensional conductors. It is shown that $r$ is proportional to $T^2$ for both free and interacting fermions. The marginal repulsive in-chain interaction acts to reduce $r$ as compared to the non-interacting result. The correction to $r$ due to the quasiparticle interaction is found as well. It scales as $T^4$ at low temperature.Comment: 5 pages, 1 eps figure; the new version of the e-print corrects an error, which exists in the original submission; fortunately, all important conclusions of the study remain vali

Significance of Operative Legal Investigation as the Criterion of Reasonable Term Definition

The article is devoted to the problem of tardiness of criminal procedure which can lead to breaches of human rights self-dependently

Ballistic dynamics of a convex smooth-wall billiard with finite escape rate along the boundary

We focus on the problem of an impurity-free billiard with a random position-dependent boundary coupling to the environment. The response functions of such an open system can be obtained non-perturbatively from a supersymmetric generating functional. The derivation of this functional is based on averaging over the escape rates and results in a non-linear ballistic $\sigma$-model, characterized by system-specific parameters. Particular emphasis is placed on the {}``whispering gallery modes'' as the origin of surface diffusion modes in the limit of large dimensionless conductance.Comment: 12 pages, no figure

Tkachenko modes and quantum melting of Josephson junction type of vortex array in rotating Bose-Einstein condensate

Using path integral formalism, we show that the Abrikosov-Tkachenko vortex lattice may equivalently be understood as an array of Josephson junctions. The Tkachenko modes are found to be basically equivalent to the low energy excitations (Goldstone modes) of an ordered state. The calculated frequencies are in very good agreement with recent experimental data. Calculations of the fluctuations of the relative displacements of the vortices show that vortex melting is a result of quantum fluctuations around the ordered state due to the low energy excitations (Tkachenko modes)and occurs when the ratio of the kinectic energy to the potential energy of the vortex lattice is 0.001.Comment: revised paper 11 pages with 2 figures, all in Pdf forma

Feasibility of a Small, Rapid Optical-to-IR Response, Next Generation Gamma Ray Burst Mission

We present motivations for and study feasibility of a small, rapid optical to IR response gamma ray burst (GRB) space observatory. By analyzing existing GRB data, we give realistic detection rates for X-ray and optical/IR instruments of modest size under actual flight conditions. Given new capabilities of fast optical/IR response (about 1 s to target) and simultaneous multi-band imaging, such an observatory can have a reasonable event rate, likely leading to new science. Requiring a Swift-like orbit, duty cycle, and observing constraints, a Swift-BAT scaled down to 190 square cm of detector area would still detect and locate about 27 GRB per yr. for a trigger threshold of 6.5 sigma. About 23 percent of X-ray located GRB would be detected optically for a 10 cm diameter instrument (about 6 per yr. for the 6.5 sigma X-ray trigger).Comment: Elaborated text version of a poster presented at 2012 Malaga/Marbella symposiu

Strong quantum fluctuation of vortices in the new superconductor MgB2MgB_2

By using transport and magnetic measurement, the upper critical field $H_{c2}(T)$ and the irreversibility line $H_{irr}(T)$ has been determined. A big separation between $H_{c2}(0)$ and $H_{irr}(0)$ has been found showing the existence of a quantum vortex liquid state induced by quantum fluctuation of vortices in the new superconductor $MgB_2$. Further investigation on the magnetic relaxation shows that both the quantum tunneling and the thermally activated flux creep weakly depends on temperature. But when the melting field $H_{irr}$ is approached, a drastic rising of the relaxation rate is observed. This may imply that the melting of the vortex matter at a finite temperature is also induced by the quantum fluctuation of vortices.Comment: 4 pages, 4 figure

Тенденции и перспективы социально-экономического развития Пермского края

Purpose: the main purpose of the article is study the current prerequisites and trends of the economic development of the Perm Region to formulate proposals and recommendations within the framework of the program for the long-term development of regional social and economic systems. The main hypothesis of the article is that the social and economic development of the Perm Region requires the creation of innovative ways to develop promising areas of business based on relevant trends and assumptions.Methods: the methodology of solving the tasks is based on the use of the method of dialectical research, methods of economic analysis, forecasting, situational and system analysis, expert assessments and analysis of empirical data.Results: the results of the work are to study the economic processes in the region, including indicators and indicators of the region's social and economic development, and further develop recommendations and proposals for the development of priority areas in project management and selection of optimal project planning models to ensure sustainable development of the region and its competitiveness.Conclusions and Relevance: priority goals for solving the current economic problems of the Perm Region are to increase the income of the population and increase the revenue of the regional budget. To increase the pace and ensure the stability of economic growth, increase the real income of citizens, achieve technological leadership, a consistent solution to a number of specific tasks is necessary. It is important that the implementation of economic policy should be based on building partnerships between public authorities and entrepreneurship, aimed at increasing the efficiency of companies and the development of the economy of the region.Цель: Основной целью настоящей статьи является исследование современных предпосылок и тенденций экономического развития Пермского края для формирования предложений и рекомендаций в рамках выявления перспектив развития региональных социально-экономических систем. Основная гипотеза статьи состоит в том, что социально-экономическое развитие Пермского края требует формирования инновационных путей развития перспективных направлений бизнеса на основании существующих в регионе тенденций и предпосылок.Методология проведения работы: Методология решения поставленных в статье задач основывается на использовании метода диалектического исследования, методов экономического анализа, прогнозирования, методов ситуационного и системного анализа, экспертных оценок и анализа эмпирических данных.Результаты работы, а также ее практическая значимость заключаются в изучении процессов экономики края, включая показатели и индикаторы социально-экономического развития региона, и последующем формировании рекомендаций и предложений по развитию приоритетных направлений в управлении проектами и выбору оптимальных моделей планирования проектов для обеспечения устойчивого развития региона и его конкурентоспособности.Выводы: Приоритетными целями для решения современных экономических проблем Пермского края являются увеличение дохода населения и увеличение дохода бюджета региона. Для повышения темпа и обеспечения стабильности экономического роста, увеличения реального дохода граждан, достижения технологического лидерства, необходимо последовательное решение ряда определенных задач. Важно, что осуществление экономической политики должно быть основано на выстраивании партнерских отношений между органами государственной власти и предпринимательством, нацеленных на увеличение эффективности работы компаний и развитие экономики края