R2R^2 inflation to probe non-perturbative quantum gravity

It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, $R+R^2$, or shortly $R^2$, inflation is the most successful in accounting for the latest CMB data from the PLANCK satellite and other experiments. Moreover, recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric space-times. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant. We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local $R^2$ model. We further compute the full second order perturbed action around any background belonging to that class. We proceed by extracting the key inflationary parameters of our model such as a spectral index ($n_s$), a tensor-to-scalar ratio ($r$) and a tensor tilt ($n_t$). It appears that $n_s$ remains the same as in the local $R^2$ inflation in the leading slow-roll approximation, while $r$ and $n_t$ get modified due to modification of the tensor power spectrum. This class of models allows for any value of $r<0.07$ with a modified consistency relation which can be fixed by future observations of primordial $B$-modes of the CMB polarization. This makes the UV complete $R^2$ gravity a natural target for future CMB probes.Comment: 37 page

Plasmonic shock waves and solitons in a nanoring

We apply the hydrodynamic theory of electron liquid to demonstrate that a circularly polarized radiation induces the diamagnetic, helicity-sensitive dc current in a ballistic nanoring. This current is dramatically enhanced in the vicinity of plasmonic resonances. The resulting magnetic moment of the nanoring represents a giant increase of the inverse Faraday effect. With increasing radiation intensity, linear plasmonic excitations evolve into the strongly non-linear plasma shock waves. These excitations produce a series of the well resolved peaks at the THz frequencies. We demonstrate that the plasmonic wave dispersion transforms the shock waves into solitons. The predicted effects should enable multiple applications in a wide frequency range (from the microwave to terahertz band) using optically controlled ultra low loss electric, photonic and magnetic devices.Comment: 13 pages, 12 figure

Тенденции развития рынка цифровых финансовых активов в контексте цифровой трансформации мировой экономики

The study focuses on identifying the driving forces behind the digital transformation of the economy in the financial sector and the development of the digital financial assets (DFA) market. The subject of the research is the factors of digital transformation and the DFA market. The relevance is due to the transformation of the world economy, associated, among other things, with the active development of the DFA market, the expansion of the possibilities of using distributed ledger technologies (DLT) and blockchain against the background of high growth rates of the cryptoasset market. The aim of the paper is to summarize the main trends in the development of the global cryptoasset market, determine the main factors of investment attractiveness of cryptocurrencies and explore the conditions for the successful implementation of various models of digital currencies of central banks (CBDC). In the course of the work, the methods of systematization and classification of information, multivariate statistical analysis were used. As a result of the study, 5 clusters of cryptocurrencies were identified, depending on the dominance in the market and the dynamics of price changes. The resulting functions can be used to predict the attribution of cryptocurrencies to the corresponding clusters. Among the factors that have a significant impact on the development of CBDC projects in general and with the wholesale model in particular, one can single out “capital”. At the same time, CBDC projects with a retail model are actively and successfully implemented in countries with a high level of technical knowledge and entrepreneurial talent, ahead of the capital factor in their importance. Taking into account the review of global trends, the development of fintech technologies, it was concluded that the processes of digitalization of financial assets are inevitable, the emergence of new forms of digital assets that dictate the need for the advanced development of their legal regulation.Исследование посвящено вопросу выявления движущих сил цифровой трансформации экономики в финансовой сфере и развитию рынка цифровых финансовых активов (ЦФА). Предметом исследования являются факторы цифровой трансформации и рынок ЦФА. Актуальность обусловлена трансформацией мировой экономики, связанной, в том числе, с активным развитием рынка ЦФА, расширением возможностей применения технологий распределенных реестров (DLT) и блокчейн на фоне высоких темпов роста рынка криптоактивов. Цель исследования — обобщить основные тенденции развития мирового рынка криптоактивов, определить основные факторы инвестиционной привлекательности криптовалют и исследовать условия успешного внедрения различных моделей цифровых валют центральных банков (CBDC). В ходе работы использованы методы систематизации и классификации информации, многомерного статистического анализа. В результате исследования выделено 5 кластеров криптовалют в зависимости от доминирования на рынке и динамики изменениях цен. Полученные функции могут быть использованы для прогноза отнесения криптовалют к соответствующим кластерам. Среди факторов, оказывающих существенное влияние на развитие проектов CBDC в общем и с оптовой моделью в частности, можно выделить «капитал». При этом проекты CBDC с розничной моделью активно и успешно реализуются в странах с высоким уровнем технических знаний и предпринимательского таланта, опережая в своем значении фактор капитала. С учетом обзора мировых тенденций, развития финтех-технологий сделан вывод о неотвратимости процессов цифровизации финансовых активов, появлении новых форм цифровых активов, диктующих необходимость опережающего развития их нормативно-правового регулирования

Radiation Due to Josephson Oscillations in Layered Superconductors

We derive the power of direct radiation into free space induced by Josephson oscillations in intrinsic Josephson junctions of highly anisotropic layered superconductors. We consider the super-radiation regime for a crystal cut in the form of a thin slice parallel to the c-axis. We find that the radiation correction to the current-voltage characteristic in this regime depends only on crystal shape. We show that at large enough number of junctions oscillations are synchronized providing high radiation power and efficiency in the THz frequency range. We discuss crystal parameters and bias current optimal for radiation power and crystal cooling.Comment: 4 pages, 1 figure, to be published in Phys. Rev. Let