Detection of acceleration radiation in a Bose-Einstein condensate

We propose and study methods for detecting the Unruh effect in a Bose-Einstein condensate. The Bogoliubov vacuum of a Bose-Einstein condensate is used here to simulate a scalar field-theory, and accelerated atom dots or optical lattices as means for detecting phonon radiation due to acceleration effects. We study Unruh's effect for linear acceleration and circular acceleration. In particular, we study the dispersive effects of the Bogoliubov spectrum on the ideal case of exact thermalization. Our results suggest that Unruh's acceleration radiation can be tested using current accessible experimental methods.Comment: 5 pages, 3 figure

THE INFLUENCE OF THE DIGITAL ECONOMY ON THE DEVELOPMENT OF THE DOMESTIC ECONOMY

The article examines the problems and prospects for the development of the digital economy in Ukraine. The current trends of new technological solutions and opportunities are identified, because global informatization intensifies this process. The effective use of digital economy tools, the means of which is to ensure information security and stability in the country, is described.The article examines the problems and prospects for the development of the digital economy in Ukraine. The current trends of new technological solutions and opportunities are identified, because global informatization intensifies this process. The effective use of digital economy tools, the means of which is to ensure information security and stability in the country, is described

Technological and methodical aspects of representation of the educational mathematical information in digital educational resources

В статье поднимаются вопросы организации математической информации на экране монитора ПК. Проводится сравнение бумажных и компьютерных образовательных ресурсов и выявляются причины, тормозящие информатизацию учебного процесса. Даётся представление о концепции, на основе которой создаются компьютерные миниатюры, разрабатываемые авторскими коллективами Визуальной школы (vischool.rxt.ru).In article questions of the organization of the mathematical information on the computer screen are brought up. Comparison of paper and computer educational resources is spent, and the reasons, braking informatization of educational process, are established. Representation the concept, basis of the computer miniatures, is given. These miniatures are created by groups of authors from «Visual school» (vischool.rxt.ru)

Interplay between charge-lattice interaction and strong electron correlations in cuprates: phonon anomaly and spectral kinks

We investigate the interplay between strong electron correlations and charge-lattice interaction in cuprates. The coupling between half breathing bond stretching phonons and doped holes in the t-t'-J model is studied by limited phonon basis exact diagonalization method. Nonadiabatic electron-phonon interaction leads to the splitting of the phonon spectral function at half-way to the zone boundary at $\vec{q}_s=\{(\pm \pi / 2, 0), (0, \pm \pi / 2) \}$ and to low energy kink feature in the electron dispersion, in agreement with experimental observations. Another kink due to strong electron correlation effects is observed at higher energy, depending on the strength of the charge-lattice coupling.Comment: 4 pages, 3 figure

Modes of Oscillation in Radiofrequency Paul Traps

We examine the time-dependent dynamics of ion crystals in radiofrequency traps. The problem of stable trapping of general three-dimensional crystals is considered and the validity of the pseudopotential approximation is discussed. We derive analytically the micromotion amplitude of the ions, rigorously proving well-known experimental observations. We use a method of infinite determinants to find the modes which diagonalize the linearized time-dependent dynamical problem. This allows obtaining explicitly the ('Floquet-Lyapunov') transformation to coordinates of decoupled linear oscillators. We demonstrate the utility of the method by analyzing the modes of a small `peculiar' crystal in a linear Paul trap. The calculations can be readily generalized to multispecies ion crystals in general multipole traps, and time-dependent quantum wavefunctions of ion oscillations in such traps can be obtained.Comment: 24 pages, 3 figures, v2 adds citations and small correction

Solid state amorphization in a thin Fe-Si-Mg-O surface film triggered by the reduction of elements from oxides in the temperature range of the α-γ transformation

The study of the processes occurring in the surface layer of the MgO coated commercial alloy Fe-3%Si-0.5%Cu (grain oriented electrical steel) demonstrated that the amorphous phase in the form of a Fe-based solid solution is formed during continuous heating in the 95%N2 + 5%H2 atmosphere. For the purposes of this study, the following methods were used: non-ambient XRD at 20 –1060°C with heating and cooling at a rate of 0.5 dps, layer-by-layer chemical analysis performed by a glow discharge analyzer, scanning electron microscopy and energy dispersive X-ray spectroscopy. ThermoCalc software was used to calculate the potential phase equilibrium states. The amorphous phase was formed in the α → γ transformation temperature range, when the heating rates were altered in the surface layer of 1 µm initially consisted of a solid α-Fe-based solution with ~1– 2 wt.% Si with (MgFe)2 SiO4, (MgFe)O, SiO2 oxide inclusions. We suppose that (MgFe)2 SiO4 oxides are partly reduced by H2 to Mg2 Si molecular complexes, which become solid solutions in the temperature range of the metastability of the α-Fe crystal lattice with subsequent amorphization as an alternative to the α → γ transition. The amorphous state is obtained at 920 – 960°C and is retained both at subsequent heating (to 1060°C) and cooling (to 20°С), which is super-stable compared to the established metallic glasses. The composition of the amorphous phase can be described by the formula Fe89.5 Si6 Mg4 Cu0.5. © 2020, Institute for Metals Superplasticity Problems of Russian Academy of Sciences. All rights reserved.Russian Foundation for Basic Research, RFBR: 20‑08‑00332Ministry of Education and Science of the Russian Federation, Minobrnauka: 11.1465.2014/K.Acknowledgements. This study was conducted using equipment provided by the Laboratory of Structural Analysis Techniques and Materials and Nanomaterials Properties of CKP Ural Federal University. The study was financially supported by Government Decree No. 211 of the Russian Federation, Contract No. 02. A03.21.0006 and within the framework of the state task issued by the Ministry of Education and Science of the Russian Federation, project No. 11.1465.2014/K. The reported study was funded by RFBR, project number 20‑08‑00332

Thermodynamics and Evaporation of the 2+1-D Black Hole

The properties of canonical and microcanonical ensembles of a black hole with thermal radiation and the problem of black hole evaporation in 3-D are studied. In 3-D Einstein-anti-de Sitter gravity we have two relevant mass scales, $m_c=1/G$, and $m_p=(\hbar^2\Lambda/G)^{1/3}$, which are particularly relevant for the evaporation problem. It is argued that in the `weak coupling' regime $\Lambda<(\hbar G)^{-2}$, the end point of an evaporating black hole formed with an initial mass $m_0>m_p$, is likely to be a stable remnant in equilibrium with thermal radiation. The relevance of these results for the information problem and for the issue of back reaction is discussed. In the `strong coupling' regime, $\Lambda>(\hbar G)^{-2}$ a full fledged quantum gravity treatment is required. Since the total energy of thermal states in anti-de Sitter space with reflective boundary conditions at spatial infinity is bounded and conserved, the canonical and microcanonical ensembles are well defined. For a given temperature or energy black hole states are locally stable. In the weak coupling regime black hole states are more probable then pure radiation states.Comment: 11 pages, TAUP 2141/94, Late

Continuous input nonlocal games

We present a family of nonlocal games in which the inputs the players receive are continuous. We study three representative members of the family. For the first two a team sharing quantum correlations (entanglement) has an advantage over any team restricted to classical correlations. We conjecture that this is true for the third member of the family as well.Comment: Journal version, slight modification