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The decay widths of $V \to K(\pi) l \bar{\nu}_l $ are calculated within the Nambu--Jona-Lasinio model, where $V=K^*, \rho, \omega, \phi$ and $l=\mu, e$. The results are obtained using the previously fixed model parameters without introducing any arbitrary parameters. The obtained results are considered as predictions due to the absence of experimental data., Comment: 7 pages, 2 figures

It is shown that the processes $e^+ e^- \to \pi^+ \pi^-$ and $\tau^- \to \pi^- \pi^0 \nu_\tau$ can be described in a unified approach in satisfactory agreement with experiment using the vector coupling constant $g_{\rho} = 6$. In this case, in addition to quark loops, it is also necessary to take into account meson loops corresponding to the next order in $1/N_c$. These loops must be taken into account when describing the $\gamma (W) \to \rho$ transition, as well as in interaction of mesons in the final state., Comment: 10 pages, 9 figures

The generation of terawatt (TW) near-single-cycle laser pulses is of high interest for applications including attosecond science. Here we demonstrate a three-stage post-compression scheme in a non-guided geometry using He as the nonlinear medium, resulting in the generation of multi-mJ pulses with a duration of 3.7 fs. Key features of this approach are its simplicity, robustness and high stability, making it ideally suited for highly demanding applications such as attosecond-pump attosecond-probe spectroscopy (APAPS). This is demonstrated by performing two-color APAPS in Ar and Ne, where both simultaneous and sequential two-photon absorption are observed. Our approach is scalable to multi-TW powers., Comment: 9 pages, 4 figures

In the framework of the $U(3) \times U(3)$ extended Nambu-Jona-Lasinio model, the processes $e^+e^- \to K^+K^-\pi^0$ and $e^+e^- \to K^+K^-\eta$ are described taking into account both ground and first radially excited intermediate meson states. It is shown that channels with radially excited $\phi(1680)$ meson are dominant in both processes. The influence on the results of the appearance of phase factors of radially excited intermediate states, the existence of which is indicated by experimental data, is discussed., Comment: 11 pages, 7 figures

The $\tau$ lepton decays $\tau \to [K^- K^0 \pi^0, K^- K^+ \pi^-, K ^0 \bar{K^0} \pi^-] \nu_{\tau}$ are described in the $U(3) \times U(3)$ NJL quark model. The contact channel and intermediate channels with axial-vector, vector and pseudoscalar mesons are taken into account. It is shown that the strange scalar meson $K^*_0$ plays an important role in these processes in addition to the intermediate vector meson $K^*$. The obtained results are in satisfactory agreement with the recent experimental data within the experimental and theoretical uncertainties., Comment: 6 pages, 2 figures

Branching fractions of decays $\tau \to K^0 \pi^- \eta\nu_\tau$, $\tau \to K^- \pi^0 \eta\nu_\tau$, $\tau \to K^-K^0 \eta\nu_\tau$ and $\tau \to K^- \eta \eta \nu_\tau$ are calculated in the $U(3)\times U(3)$ chiral NJL quark model. The contact, vector, axial-vector and pseudoscalar channels are considered. It is shown that the axial vector channel is dominant. The obtained results are in satisfactory agreement with experiment., Comment: 7 pages, 2 figures

The widths of the decays $\tau \to K^- K^+ K^- \nu_\tau$ and $\tau \to K^- K^0 \bar{K}^0 \nu_\tau$ are calculated in the $U(3)\times U(3)$ chiral quark NJL model. Four channels are considered: contact, axial vector, vector and pseudoscalar channels. It is shown that the dominant contribution is given by the axial vector channel with an intermediate $\phi$ meson. The obtained results are in satisfactory agreement with the experimental data.

The branching fractions of $\tau \to \pi^+ \pi^-\pi^- \nu_\tau$ and $\tau \to \pi^- 2\pi^0\nu_\tau$ are calculated within the chiral NJL model. Features of the axial-vector $a_1$ meson which plays an important role in describing the $\tau$ decays are discussed. Permissible values for the mass and width of the $a_1$ meson are considered in accordance with the latest experiments., Comment: 2 figures

The branching fractions of the decays $\tau^- \to K^- \pi^+ \pi^- \nu_\tau$, $\tau^- \to K^- \pi^0 \pi^0 \nu_\tau$ and $\tau^- \to \bar{K}^0 \pi^- \pi^0\nu_\tau$ are calculated in the $U(3)\times U(3)$ Nambu--Jona-Lasinio type chiral model. Four intermediate channels are considered: the contact channel and the channels with the intermediate axial vector, vector and pseudoscalar mesons. The additional resonance states $K^* \pi$ and $K \rho$ are taken into account in all channels. It is shown that the main contributions to the widths of these decays are given by the axial vector channel. In the axial vector channel, the intermediate resonances $K_1(1270)$ and $K_1(1400)$ are taken into account. The obtained results are in satisfactory agreement with the known experimental data., Comment: 7 pages, 2 figures

Decays of scalar mesons $K^*_0(800) \to K\pi$ and $K^*_0(1430) \to K\pi, K \eta, K \eta', K_1 \pi$ are described in the extended $U(3 ) \times U(3)$ Nambu - Jona-Lasinio chiral quark model. The obtained results are in satisfactory agreement with the new experimental data obtained by the BaBar collaboration, which markedly differ from the existing values in the PDG., Comment: 6 pages, 1 figure

In this work, we synthesize and investigate lower technetium hydrides at pressures up to 45 GPa using the synchrotron X-ray diffraction, reflectance spectroscopy, and ab initio calculations. In the Tc-H system, the hydrogen content in TcH$_x$ phases increases when the pressure rises, and at 27 GPa we found a new hexagonal (hcp) nonstoichiometric hydride TcH$_{1.3}$. The formation of technetium hydrides is also confirmed by the emergence of a new reflective band at 450-600 nm in the reflectance spectra of TcH$_x$ samples synthesized at 45 GPa. On the basis of the theoretical analysis, we proposed crystal structures for the TcH$_{0.45 \pm 0.05}$ (Tc$_{16}$H$_7$) and TcH$_{0.75 \pm 0.05}$ (Tc$_4$H$_3$) phases previously obtained at 1-2 GPa. The calculations of the electron-phonon interaction show that technetium hydrides TcH$_{1+x}$ do not possess superconducting properties due to the low electron-phonon interaction parameter ($\lambda \sim 0.23$).

We show that it is co-NP-hard to check whether a given semigroup identity holds in the twisted Brauer monoid $\mathcal{B}^\tau_n$ with $n\ge5$., Comment: 20 pages, 5 figures. In v2, several typos and inaccuracies are corrected, and a few suggestions by the anonymous referee are implemented

The branching fraction of the decay $\eta' \to \pi\rho$ is calculated in the chiral quark NJL model. The decay exists due to the mass difference between $u$- and $d$-quarks leading to $\pi^{0}-\eta^{'}$ mixing. Two different approaches are applied: the approximate calculation of this process taking into account the transition $\pi^{0}-\eta^{'}$ explicitly without dioganalisation and a more precise approach consisting in the diagonalisation of the singlet and octet states leading to the physical fields $\pi^{0}$, $\eta$ and $\eta^{'}$. The obtained results are in satisfactory agreement with current experimental data.

In the extended $U(3)\times U(3)$ NJL model, semileptonic decays of $\rho$, $\omega$, $\phi$, $\eta$ and $\eta'$ mesons in both the ground and first radially excited states are described. Quark loops of the anomalous type are considered, which are based on the vertex $\eta \to VV$. The obtained results are in satisfactory agreement with the existing experimental data. In addition, a number of predictions for experimentally unmeasured decays of radially excited mesons are presented., Comment: 6 pages, 2 figures

The $U(3) \times U(3)$ chiral symmetric NJL model describing pseudoscalar, vector, and axial vector mesons in both the ground state and first radially excited states is shortly presented in this review. In this model, it is possible to describe a large number of low-energy interactions of mesons, $\tau$ lepton decays into mesons and processes of meson production in electron-positron annihilations in satisfactory agreement with the experiments. In describing a number of processes, it turned out to be necessary to take into account the interactions of mesons in the final state., Comment: 62 pages, 32 figures and 8 tables

The branching fraction of the decay $\tau \to K^{-} K^{0} \nu_{\tau}$ is calculated in the framework of the extended Nambu--Jona-Lasinio model. The contact and vector channels are considered. The contributions to this process of the $\rho$ meson in the ground and first radially excited states are taken into account in the vector channel. The obtained results are in satisfactory agreement with the experimental data. Taking into account the kaon interaction in the final state results in insignificant corrections, which are not beyond the scope of the model uncertainties.

The effect of the interaction of mesons in the final state is additionally considered within the description of $\tau \to \pi \eta(\eta') \nu_{\tau}$ decays. This interaction is taken into account at the level of production of intermediate pions. One of them, in turn, might be transited into $\eta$ or $\eta'$ mesons. Our results do not exceed the experimentally established branching fractions, and they are in agreement with the results of other theoretical studies., Comment: 9 pages, 2 figures

The branching fraction of the decay $\tau \to K^{-} \eta \nu_{\tau}$ has been calculated by using the extended Nambu-Jona-Lasinio model taking into account the meson interaction in the final state. The contact term and the channel with the intermediate ground $K^{*}(892)$ and first radially excited state $K^{*}(1410)$ have been calculated. For the purpose of describing the meson interaction in the final state, the triangle diagram with three mesons has been considered. The cutoff parameter of divergent integrals of the meson loop is equal to the appropriate parameter used in our previous work to describe the decay $\tau \to K^{-} \pi^{0} \nu_{\tau}$. Thereby, the present work does not set any additional arbitrary parameters. The obtained results are in satisfactory agreement with the experimental data.

Magnetic phenomena are ubiquitous in our surroundings and indispensable for modern science and technology, but it is notoriously difficult to change the magnetic order of a material in a rapid way. However, if a thin nickel film is subjected to ultrashort laser pulses, it can lose its magnetic order almost completely within merely femtosecond times. This phenomenon, in the meantime also observed in many other materials, has connected magnetism with femtosecond optics in an efficient, ultrafast and complex way, offering opportunities for rapid information processing or ultrafast spintronics at frequencies approaching those of light. Consequently, the physics of ultrafast demagnetization is central to modern material research, but a crucial question has remained elusive: If a material loses its magnetization within only femtoseconds, where is the missing angular momentum in such short time? Here we use ultrafast electron diffraction to reveal in nickel an almost instantaneous, long-lasting, non-equilibrium population of anisotropic high-frequency phonons that appear as quickly as the magnetic order is lost. The anisotropy plane is perpendicular to the direction of the initial magnetization and the atomic oscillation amplitude is 2 pm. We explain these observations by means of circularly polarized phonons that quickly absorb the missing angular momentum of the spin system before the slower onset of a macroscopic sample rotation. The time that is needed for demagnetization is related to the time it takes to accelerate the atoms. These results provide an atomistic picture of ultrafast demagnetization under adherence to all conservation laws but also demonstrate the general importance of polarized phonons for non-equilibrium dynamics and provide innovative ways for controlling materials on atomic dimensions.

In this work, we argue that the observed differences in the value of the vector coupling constant extracted from the decays $\rho\to \pi\pi$ ($g_{\rho} = 6.0$), $\rho\to l^+l^-$ ($g_{\rho} = 5.0 $) and $\omega\to l^+ l^-$ ($g_{\rho} = 5.7$), where $l=e,\mu $, are an indication of the important role played by the $1/N_c$ corrections in the description of these processes. We show that an emission of a photon by charged meson loops in the $\rho^0, \omega,\phi\to\gamma$ transitions is a key process that allows to describe above vector meson decays into two leptons with a single value $g_\rho = 6.0$. Our result supports the idea of universality of neutral vector mesons and clarifies the role of accounting of $1/N_c$ corrections to its fulfilment., Comment: 9 pages, 2 figuras, the version accepted for publication in Physical Review D

The possibility to use the width of the decay $\rho \to e^{+}e^{-}$ to fix the input parameter $g_\rho=5.0$ of the $SU(2) \times SU(2)$ chiral-symmetric Nambu--Jona-Lasinio model is discussed. It is shown that for a consistent simultaneous description of the processes $\rho \to e^{+}e^{-}$, $\rho \to \pi^{+}\pi^{-}$, $\tau^{-} \to \pi^{-}\pi^{0} \nu_{\tau}$, and $e^{+}e^{-} \to \pi^{+}\pi^{-}$ can be constructed. Taking into account the interaction of pions in the final state appears to be important. The obtained theoretical results for the considered processes are in a satisfactory agreement with experimental data., Comment: 4 pages, 6 figures, misprints are corrected

The processes $\tau^- \to \pi^- \pi^0 \nu_{\tau}$ and $e^{+}e^{-} \to \pi^{+} \pi^{-}$ are considered within the chiral Nambu--Jona-Lasinio model with taking into account the pion final state interactions beyond the leading $1/N_c$ approximation. The contribution of the loop correction caused by a $\rho$ meson exchange between the pions, which gives the main contribution in the P-wave channel, is caclulated. The results for both processes are in a satisfactory agreement with experimental data., Comment: 8 pages, 8 figures, formula (10) is corrected, numerical results are slightly changed

We study the low-temperature electrical and thermal conductivity of CoSi and Co$_{1-x}$M$_x$Si alloys (M = Fe, Ni; $x \leq$ 0.06). Measurements show that the low-temperature electrical conductivity of Co$_{1-x}$Fe$_{x}$Si alloys decreases at $x > $ 0.01 by an order of magnitude compared with that of pure CoSi. It was expected that both the lattice and electronic contributions to thermal conductivity would decrease in the alloys. However, our experimental results revealed that at temperatures below 20K the thermal conductivity of Fe- and Ni-containing alloys is several times larger than that of pure CoSi. We discuss possible mechanisms of the thermal conductivity enhancement. The most probable one is related to the dominant scattering of phonons by charge carriers. We propose a simple theoretical model that takes into account the complex semimetallic electronic structure of CoSi with nonequivalent valleys, and show that it explains well the increase of the lattice thermal conductivity with increasing disorder and the linear temperature dependence of the thermal conductivity in the Co$_{1-x}$Fe$_x$Si alloys below 20K., Comment: 10 pages, 6 figures

In the present work, the mixing angle of the vector $\omega(782)$ and $\phi(1020)$ mesons is estimated in the framework of Nambu--Jona-Lasinio model. The decay $\phi \to \pi^{0} \gamma$ is considered as a basic process to determine this angle. The obtained value is compared with the results of the other authors. Besides, the width of the decay $\phi \to 3\pi$ and the cross-section of the process $e^{+}e^{-} \to \pi^{0} \phi$ are calculated by using this angle.

The rates and spectra of the anomalous $\eta\to\pi^+\pi^-\gamma$ and $\eta' \to\pi^+\pi^-\gamma$ decays are calculated. The approach is based on the effective meson Lagrangian obtained in the Nambu-Jona-Lasinio model with vector and axial-vector mesons by integrating out quark fields. The resulting action is affected by mixing between members of pseudoscalar $J^{PC}=0^{-+}$ and axial-vector $1^{++}$ nonets that violates some low-energy theorems. In this note we point out that a gauge covariant procedure to diagonalize this mixing allows for consistent description of the $\eta\to\pi^+\pi^-\gamma$ and $\eta' \to\pi^+\pi^-\gamma$ decays., Comment: 8 pages, 6 figuras

In the extended Nambu -- Jona-Lasinio model, the decay width of $\tau \to K^{*0}(892) K^- \nu_{\tau}$ is calculated. The contributions from the contact diagram and diagrams with intermediate axial-vector, vector and pseudoscalar mesons in the ground and first radially excited states are taken into account. It is shown that axial-vector and vector channel with a contact diagram give a dominant contribution to the decay width. The obtained results for the decay width $\tau \to K^{*0}(892) K^- \nu_{\tau}$ are in satisfactory agreement with experimental data. A prediction for differential distribution over the invariant mass of the meson pair $K^{*0}(892) K^-$ is given., Comment: 7 pages, 3 figures

Locally inverse semigroups are regular semigroups whose idempotents form pseudo-semilattices. We characterise the categories that correspond to locally inverse semigroups in the realm of Nambooripad's cross-connection theory. Further, we specialise our cross-connection description of locally inverse semigroups to inverse semigroups and completely 0-simple semigroups, obtaining structure theorems for these classes. In particular, we show that the structure theorem for inverse semigroups can be obtained using only one category, quite analogous to the Ehresmann-Schein-Nambooripad Theorem; for completely 0-simple semigroups, we show that cross-connections coincide with structure matrices, thus recovering the Rees Theorem by categorical tools.

The decay width $\tau \to K^{*-}(892) \eta \nu_{\tau}$ was calculated in the Nambu--Jona-Lasinio model. Four channels were taken into account: the contact channel (the final states are directly producted from lepton current without any intermediate meson states), the axial-vector channel with two intermediate physical states $K_{1}(1270)$ and $K_{1}(1400)$, the vector channel with intermediate $K^{*}(892)$ meson and the pseudoscalar channel with intermediate $K$ meson. It is shown that the first two channels give the dominant contribution to the decay width. Of the remaining two channels, the pseudoscalar channel plays a more prominent role. The final result is in satisfactory agreement with experimental data. Prediction for the differential decay width is presented., Comment: 4 pages, 3 figures

Kauffman monoids $\mathcal{K}_n$ and Jones monoids $\mathcal{J}_n$, $n=2,3,\dots$, are two families of monoids relevant in knot theory. We prove a somewhat counterintuitive result that the Kauffman monoids $\mathcal{K}_3$ and $\mathcal{K}_4$ satisfy exactly the same identities. This leads to a polynomial time algorithm to check whether a given identity holds in $\mathcal{K}_4$. As a byproduct, we also find a polynomial time algorithm for checking identities in the Jones monoid $\mathcal{J}_4$., Comment: 25 pages, 7 figures

In the extended Nambu--Jona-Lasinio model, the decay widths of the processes $\tau \to [\omega(782), \phi(1020)] K^{-} \nu_{\tau}$ were calculated. The intermediate channels with axial vector ($K_{1}(1270)$, $K_{1}(1400)$ and $K_{1}(1650)$), vector ($K^{*}(892)$ and $K^{*}(1410)$) and pseudoscalar ($K$ and $K(1460)$) mesons were considered. The results for these processes are in satisfactory agreement with the experimental data.

In the extended NJL model, the decay widths of $\tau\rightarrow (K, K(1460))\nu_{\tau}$, $(K, K(1460))\rightarrow {\mu}\nu_{\mu}$ are calculated. The contributions from intermediate axial-vector mesons ${K}_{1}(1270)$, ${K}_{1}(1400)$ and the first radially excited state ${K}_{1}(1650)$ are taken into account. Estimates for the weak decay coefficients ${F}_{K}$ and ${{F}_{{K}^{'}}}$ are given. Predictions are made for the width of $\tau\rightarrow K(1460)\nu_{\tau}$ decay and ${{F}_{{K}^{'}}}$ constant., Comment: 8 pages, 4 figures

In the extended Nambu--Jona-Lasinio model, the decay widths of the processes $\tau \to [\omega(782), \phi(1020)] K^{-} \nu_{\tau}$ were calculated. The intermediate strange quark-antiquark mesons in both the ground and the first radially excited states were taken into account. The meson $K_{1}(1400)$, being a possible candidate for the role of the tetraquark meson, was also taken into account as an intermediate state. The result for the process $\tau \to \omega(782) K^{-} \nu_{\tau}$ is in satisfactory agreement with the experimental data. Simultaneously, the result for the decay $\tau \to \phi(1020) K^{-} \nu_{\tau}$ is in agreement with the experimental data with precision $1.3 \sigma$., Comment: Another explanation of the nature of the physical state $K_{1}(1400)$ was found

We give a transparent combinatorial characterization of the identities satisfied by the Kauffman monoid $\mathcal{K}_3$. Our characterization leads to a polynomial time algorithm to check whether a given identity holds in $\mathcal{K}_3$., Comment: 16 pages. The referee's suggestions have been taken into account

Nanosized Y3Fe5O12 epitaxial films have been grown on Nd3Ga5O12 substrates using laser molecular beam epitaxy method. Magneto-optical polar Kerr effect, ferromagnetic resonance and spin wave propagation measurements show that the stress-related anisotropy field has an opposite sign, compared to that in the YIG/GGG systems. This leads to a considerable decrease of the effective magnetization that opens a perspective to get YIG films with perpendicular magnetization for utilizing forward volume spin waves. Longitudinal magnetooptical Kerr effect magnetometry reveals a large contribution of quadratic in magnetization terms into dielectric permittivity tensor at optical frequencies. This effect strongly increases with temperature decrease and is explained by magnetization of the interface Nd3+ ions that are exchange coupled to the Fe3+ ions., Comment: 10 pages, 4 figures