Asymptotically maximal families of hypersurfaces in toric varieties

A real algebraic variety is maximal (with respect to the Smith-Thom inequality) if the sum of the Betti numbers (with $\mathbb{Z}_2$ coefficients) of the real part of the variety is equal to the sum of Betti numbers of its complex part. We prove that there exist polytopes that are not Newton polytopes of any maximal hypersurface in the corresponding toric variety. On the other hand we show that for any polytope $\Delta$ there are families of hypersurfaces with the Newton polytopes $(\lambda\Delta)_{\lambda \in \mathbb{N}}$ that are asymptotically maximal when $\lambda$ tends to infinity. We also show that these results generalize to complete intersections.Comment: 18 pages, 1 figur

Consideration of unresolved binaries with evaluation of the mass of star clusters

При различных предположениях о функции масс компонент двойных систем оценивается, как наличие неразрешенных двойных систем влияет на определение массы скопления.An influence of the presence of unresolved binaries onto star cluster mass estimation is evaluated with different assumptions on the mass function of binary components.Часть работ проведена при финансовой поддержке государства в лице Министерства образования и науки Российской Федерации (базовая часть госзадания, РК №AAAA-A17-117030310283-7), а также при финансовой поддержке Правительства РФ (постановление № 211, контракт № 02.A03.21.0006)

Radio-frequency Bloch-transistor electrometer

A quantum-limited electrometer based on charge modulation of the Josephson supercurrent in the Bloch transistor inserted into a superconducting ring is proposed. As this ring is inductive coupled to a high-Q resonance tank circuit, the variations of the charge on the transistor island (input signal) are converted into variations of amplitude and phase of radio-frequency oscillations in the tank. These variations are amplified and then detected. The output noise, the back-action fluctuations and their cross-correlation are computed. It is shown that our device enables measurements of the charge with a sensitivity which is determined by the energy resolution of its amplifier, that can be reduced down to the standard quantum limit of \hbar/2. On the basis of this setup a "back-action-evading" scheme of the charge measurements is proposed.Comment: 5 pages incl. 2 figure

Unresolved Multiple Stars and Galactic Clusters' Mass Estimates

If not properly accounted for, unresolved binary stars can induce a bias in the photometric determination of star cluster masses inferred from star counts and the luminosity function. A correction factor close to 1.15 (for a binary fraction of 0.35) was found in Borodina et al., which needs to be applied to blind photometric mass estimates. This value for the correction factor was found to be smaller than literature values. In an attempt to lift this discrepancy, in this work the focus is on higher order multiple stars with the goal of investigating the effect of triple and quadruple systems adopting the same methodology and data set as in the quoted work. The result is that when triple and quadruple, together with binary, systems are properly accounted for, the actual cluster mass (computed as all stars were single) should be incremented by a factor of 1.18-1.27, depending on the cluster and when the binary fraction α is 0.35. Fitting formulae are provided to derive the increment factor for different binary star percentages. © 2021. The American Astronomical Society. All rights reserved.

Acceleration of the precession frequency for optically-oriented electron spins in ferromagnetic/semiconductor hybrids

Time-resolved Kerr rotation measurements were performed in InGaAs/GaAs quantum wells nearby a doped Mn delta layer. Our magneto-optical results show a typical time evolution of the optically-oriented electron spin in the quantum well. Surprisingly, this is strongly affected by the Mn spins, resulting in an increase of the spin precession frequency in time. This increase is attributed to the variation in the effective magnetic field induced by the dynamical relaxation of the Mn spins. Two processes are observed during electron spin precession: a quasi-instantaneous alignment of the Mn spins with photo-excited holes, followed by a slow alignment of Mn spins with the external transverse magnetic field. The first process leads to an equilibrium state imprinted in the initial precession frequency, which depends on pump power, while the second process promotes a linear frequency increase, with acceleration depending on temperature and external magnetic field. This observation yields new information about exchange process dynamics and on the possibility of constructing spin memories, which can rapidly respond to light while retaining information for a longer period.Comment: 7 pages, 5 figure

Consistent alpha-cluster description of the 12C (0^+_2) resonance

The near-threshold 12C (0^+_2) resonance provides unique possibility for fast helium burning in stars, as predicted by Hoyle to explain the observed abundance of elements in the Universe. Properties of this resonance are calculated within the framework of the alpha-cluster model whose two-body and three-body effective potentials are tuned to describe the alpha - alpha scattering data, the energies of the 0^+_1 and 0^+_2 states, and the 0^+_1-state root-mean-square radius. The extremely small width of the 0^+_2 state, the 0_2^+ to 0_1^+ monopole transition matrix element, and transition radius are found in remarkable agreement with the experimental data. The 0^+_2-state structure is described as a system of three alpha-particles oscillating between the ground-state-like configuration and the elongated chain configuration whose probability exceeds 0.9

КВАНТОВО-ХИМИЧЕСКОЕ МОДЕЛИРОВАНИЕ СИН-АНТИ - ИЗОМЕРИЗАЦИИ В МЕТИЛЗАМЕЩЕННЫХ АЛЛИЛЬНЫХ КОМПЛЕКСАХ НИКЕЛЯ(II)

The syn-anti isomerization of bis-(η3 -allyl)nickel complexes (allyl – C3H5, 2-CH3C3H4, 1-CH3C3H4) has been studied using the density functional theory (DFT-PBE). Calculations indicated that in all cases isomerization goes through 3 steps according to η3 -η1 -η3 -mechanism. The rate-limiting step of that is vinyl fragment rotation in η1 -allyl ligand.Методом функционала плотности DFT-PBE проведено моделирование син-анти-изомеризации в бис-η3-аллильных комплексах никеля (аллил - C3H5, 2-CH3C3H4, 1-CH3C3H4). Расчеты показали, что во всех рассмотренных случаях изомеризация протекает в три стадии по η3-η1-η3-механизму с лимитирующей стадией поворота винильного фрагмента в η1-аллильном интермедиате

Optically controlled spin-polarization memory effect on Mn delta-doped heterostrucutres

We investigated the dynamics of the interaction between spin-polarized photo-created carriers and Mn ions on InGaAs/GaAs:Mn structures. The carriers are confined in an InGaAs quantum well and the Mn ions come from a Mn delta-layer grown at the GaAs barrier close to the well. Even though the carriers and the Mn ions are spatially separated, the interaction between them is demonstrated by time-resolved spin-polarized photoluminescence measurements. Using a pre-pulse laser excitation with an opposite circular-polarization clearly reduces the polarization degree of the quantum-well emission for samples where a strong magnetic interaction is observed. The results demonstrate that the Mn ions act as a spin-memory that can be optically controlled by the polarization of the photocreated carriers. On the other hand, the spin-polarized Mn ions also affect the spin-polarization of the subsequently created carriers as observed by their spin relaxation time. These effects fade away with increasing time delays between the pulses as well as with increasing temperatures.Comment: 12 pages, 5 figure