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In this paper, we address the challenge of speech enhancement in real-world recordings, which often contain various forms of distortion, such as background noise, reverberation, and microphone artifacts. We revisit the use of Generative Adversarial Networks (GANs) for speech enhancement and theoretically show that GANs are naturally inclined to seek the point of maximum density within the conditional clean speech distribution, which, as we argue, is essential for the speech enhancement task. We study various feature extractors for perceptual loss to facilitate the stability of adversarial training, developing a methodology for probing the structure of the feature space. This leads us to integrate WavLM-based perceptual loss into MS-STFT adversarial training pipeline, creating an effective and stable training procedure for the speech enhancement model. The resulting speech enhancement model, which we refer to as FINALLY, builds upon the HiFi++ architecture, augmented with a WavLM encoder and a novel training pipeline. Empirical results on various datasets confirm our model's ability to produce clear, high-quality speech at 48 kHz, achieving state-of-the-art performance in the field of speech enhancement. Demo page: https://samsunglabs.github.io/FINALLY-page, Comment: Accepted to NeurIPS 2024

This paper introduces a speech enhancement solution tailored for true wireless stereo (TWS) earbuds on-device usage. The solution was specifically designed to support conversations in noisy environments, with active noise cancellation (ANC) activated. The primary challenges for speech enhancement models in this context arise from computational complexity that limits on-device usage and latency that must be less than 3 ms to preserve a live conversation. To address these issues, we evaluated several crucial design elements, including the network architecture and domain, design of loss functions, pruning method, and hardware-specific optimization. Consequently, we demonstrated substantial improvements in speech enhancement quality compared with that in baseline models, while simultaneously reducing the computational complexity and algorithmic latency., Comment: Accepted by Interspeech 2024

The spin current model of electric polarization of multiferroics is justified via the quantum hydrodynamic method and the mean-field part of the spin-orbit interaction. The spin current model is applied to derive the electric polarization proportional to the scalar product of the spins of the near by ions, which appears to be caused by the Dzylaoshinskii-Moriya interaction. Symmetric tensor spin structure of the polarization is discussed as well. We start our derivations for the ferromagnetic multiferroic materials and present the further generalization for the antiferromagnetic multiferroic materials. We rederive the operator of the electric dipole moment, which provides the macroscopic polarization obtained via the spin current model. Finally, we use the quantum average of the found electric dipole moment operator in order to derive the polarization evolution equation for the antiferromagnetic multiferroic materials. Possibility of spiral spin structures is analyzed., Comment: 16 pages

The research results of the microstructure and corrosion resistance of Ti and Ti-Al-V Russian industrial titanium alloys obtained by spark plasma sintering (SPS) are described. Investigations of the microstructure, phase composition, hardness, tensile strength, electrochemical corrosion resistance and hot salt corrosion of Ti-Al-V titanium alloy specimens were carried out. It was shown that the alloy specimens have a uniform highly dense microstructure and high hardness values. The studied alloys also have high resistance to electrochemical corrosion during tests in acidic aqueous solution causing the intergranular corrosion as well as high resistance to the hot salt corrosion. The assumption that the high hardness of the alloys as well as the differences in the corrosion resistance of the central and lateral parts of the specimens are due to the diffusion of carbon from the graphite mold into the specimen surface was suggested., Comment: 28 pages, 3 tables, 13 figures, 61 references

The paper considers a slightly modified one-dimensional infinite mass-in-mass chain. In the case of the long-wave approximation, which corresponds to the transition to a continuous medium, we obtained a system of two equations, which is a generalization of the classical mechanics Klein-Gordon-Fock equation and has both optical and acoustic branches of the dispersion relation. Based on this classical mechanics system of equations, we have proposed a system of two relativistic quantum mechanics equations, which is a generalization of the relativistic quantum mechanics Klein-Gordon-Fock equation. Next, based on this system and following the Dirac approach, we have proposed the generalization of the Dirac equation for a free electron with an eight-component wave function in the form of a system of eight linear partial differential equations of the first order. Unlike the Dirac equation with a four-component wave function, which has only an optical branch of the dispersion relation, the generalized Dirac equation has both optical and acoustic branches of the dispersion relation, each of which has two branches with positive and negative energies, respectively. We have calculated phase and group velocities for all cases. For the positive and negative acoustic branches, the phase and group velocities are equal in modulus to the speed of light. For the positive and negative optical branches, the phase and group velocities have a structure like that of de Broglie waves. In the one-dimensional case, eight linearly independent solutions corresponding to eight combinations of two branches of dispersion, two signs of total energy, and two possible directions of spin orientation, each in the form of four plane waves, are obtained., Comment: 12 pages, 2 figures

The multiferroics are the materials, where single cell of a magnetically order crystal forms an electric dipole moment. We derive equation for the evolution of the macroscopic density of the electric dipole moment (polarization of the system). The derivation is made within the "quantum hydrodynamic" method, which allows to derive equations for the evolution of the macroscopic functions of the quantum systems starting with the microscopic description. In this work we do not consider the microscopic level of individual electrons and ions, but we start our analysis from the combination of ions in cells of the crystal. We present an effective Hamiltonian for the evolution of such intermediate scale objects. We also apply the equation for the electric dipole moment of the single cell, which is recontracted in the corresponding operator. Using this operator and the wave function of combination of ions in the cell, we define the macroscopic density of the electric dipole moment. Finally, we apply the nonstationary Schrodinger equation with the chosen Hamiltonian in order to derive equation evolution of the polarization. The derivation is made for the dipole formed by the exchange-striction mechanism in the II-type multiferroic materials. The interaction caused term in the polarization evolution equation is found to be proportional to the fourth space derivative of mixed product (triple scalar product) of three spin density vectors. Conditions are discussed for the regime, where interaction appears in a smaller order on the space derivatives., Comment: 14 pages

The strong coupling between magnetism and ferroelectricity was found in rare earth manganites, where the electric polarization could be induced by special magnetic ordering. There is no theoretical model that would allow us to study the static and dynamic properties of electric polarization in strongly correlated magnetic dielectrics. In the presented research, we have taken the main step towards the construction of such a fundamental model, and made a direct connection between the microscopic Katsura-Nagaosa-Balatsky theory and Mostovoy's phenomenological model for magnetically induced polarization. A novel description of the ferroelectricity of spin origin is proposed within the framework of the many-particle quantum hydrodynamics method. It is applied to the study of cells of magnetic ions, where the electric dipole moment is proportional to the vector product of spins. Our approach is based on the many-particle Pauli equation, where the influence of an external magnetic field is considered. We define the electric dipole moment operator of the ion cell and introduce the macroscopic polarization as the quantum mechanical average of that operator. We formulate a model for the description of nonequilibrium polarization and derive a new polarization evolution equation. The polarization switching in ferroelectric magnets with the spiral spin-density-wave state is considered, and we demonstrate that the proposed model yields known results and can predict novel effects. The dynamic magnetoelectric effect can be investigated by employing this novel equation to study the evolution of polarization.

This paper introduces UnDiff, a diffusion probabilistic model capable of solving various speech inverse tasks. Being once trained for speech waveform generation in an unconditional manner, it can be adapted to different tasks including degradation inversion, neural vocoding, and source separation. In this paper, we, first, tackle the challenging problem of unconditional waveform generation by comparing different neural architectures and preconditioning domains. After that, we demonstrate how the trained unconditional diffusion could be adapted to different tasks of speech processing by the means of recent developments in post-training conditioning of diffusion models. Finally, we demonstrate the performance of the proposed technique on the tasks of bandwidth extension, declipping, vocoding, and speech source separation and compare it to the baselines. The codes are publicly available., Comment: Accepted to Interspeech 2023

There is a version of the Landau-Lifshitz equation that takes into account the Coulomb exchange interactions between atoms, expressed by the term $\sim\bm{s}\times\triangle\bm{s}$. On the other hand, ions in the magnetic materials have several valence electrons on the $d$-shell, and therefore the Hamiltonian of many-electron atoms with spins $S>1$ should include a biquadratic exchange interaction. We first propose a new fundamental microscopic derivation of the spin density evolution equation with an explicit form of biquadratic exchange interaction using the method of many-particle quantum hydrodynamics. The equation for the evolution of the spin density is obtained from the many-particle Schrodinger-Pauli equation and contains the contributions of the usual Coulomb exchange interaction and the biquadratic exchange. Furthermore, the derived biquadratic exchange torque in the spin density evolution equation is proportional to the nematic tensor for the medium of atoms with spin $\textit{S = 1}$. Our method may be very attractive for further studies of the magnetoelectric effect in multiferroics.

We investigate the axial vector torsion-spin coupling effects in the framework of the Poincar\'e gauge theory of gravity with the general Yang-Mills type Lagrangian. The dynamical equations for the ``electric'' and ``magnetic'' components of the torsion field variable are obtained in the general form and it is shown that the helicity density and the spin density of the electromagnetic field appear as the physical sources. The modified Maxwell's equations for the electromagnetic field are derived, and the electromagnetic wave propagation under the action of the uniform homogeneous torsion field is considered. We demonstrate the Faraday effect of rotation of the polarization for such a wave, and establish the strong bound on the possible cosmic axial torsion field from the astrophysical data., Comment: 22 pages, 1 figure, Revtex, misprints removed, references updated

Detailed deterministic derivation of the kinetic equations for the relativistic plasmas is given. Focus is made on the dynamic of one-coordinate distribution functions of various tensor dimensions, but the closed set of kinetic equations is constructed of three functions: the scalar distribution function, the vector distribution function of dipole moment, and the vector distribution function of velocity (or the dipole moment in the momentum space). All two-coordinate distributions functions are discussed as well. They are presented together with their limits existing in the self-consistent field approximation. The dynamics of the small amplitude spin-electron-acoustic waves in the dense degenerate plasmas is are studied within the kinetic model. This work presents the deterministic approach to the derivation and interpretation of the kinetic equations. So, no probability is introduced during the transition from the level of individual particles to the collective functions. Problem of thermalization is not considered, but we can see that the structure of kinetic equations is kept for the system before and after thermalization. Hence, the kinetic equations can be used to approach this item., Comment: 18 pages, 2 figures

Streaming models are an essential component of real-time speech enhancement tools. The streaming regime constrains speech enhancement models to use only a tiny context of future information. As a result, the low-latency streaming setup is generally considered a challenging task and has a significant negative impact on the model's quality. However, the sequential nature of streaming generation offers a natural possibility for autoregression, that is, utilizing previous predictions while making current ones. The conventional method for training autoregressive models is teacher forcing, but its primary drawback lies in the training-inference mismatch that can lead to a substantial degradation in quality. In this study, we propose a straightforward yet effective alternative technique for training autoregressive low-latency speech enhancement models. We demonstrate that the proposed approach leads to stable improvement across diverse architectures and training scenarios., Comment: Accepted to Interspeech 2023

The open problem of derivation of the relativistic Vlasov equation for the systems of charged particles moving with the velocities up to the speed of light and creating the electromagnetic field in accordance with the full set of the Maxwell equations is considered. Moreover, the method of derivation is firstly illustrated on the nonrelativistic kinetic model. Independent derivation of the relativistic hydrodynamics is also demonstrated. Key role of these derivations of the hydrodynamic and kinetic equations includes the explicit operator of averaging on the physically infinitesimal volume suggested by L.S. Kuzmenkov., Comment: 22 pages, 7 figures

Fast Fourier convolution (FFC) is the recently proposed neural operator showing promising performance in several computer vision problems. The FFC operator allows employing large receptive field operations within early layers of the neural network. It was shown to be especially helpful for inpainting of periodic structures which are common in audio processing. In this work, we design neural network architectures which adapt FFC for speech enhancement. We hypothesize that a large receptive field allows these networks to produce more coherent phases than vanilla convolutional models, and validate this hypothesis experimentally. We found that neural networks based on Fast Fourier convolution outperform analogous convolutional models and show better or comparable results with other speech enhancement baselines., Comment: Submitted to INTERSPEECH 2022

Generative adversarial networks have recently demonstrated outstanding performance in neural vocoding outperforming best autoregressive and flow-based models. In this paper, we show that this success can be extended to other tasks of conditional audio generation. In particular, building upon HiFi vocoders, we propose a novel HiFi++ general framework for bandwidth extension and speech enhancement. We show that with the improved generator architecture, HiFi++ performs better or comparably with the state-of-the-art in these tasks while spending significantly less computational resources. The effectiveness of our approach is validated through a series of extensive experiments., Comment: Accepted to ICASSP 2023

Propagation of the finite amplitude electromagnetic wave through the partially spin-polarized degenerate plasmas leads to the instability. The instability happens at the interaction of the electromagnetic wave with the small frequency longitudinal spin-electron-acoustic waves. Strongest instability happens in the high density degenerate plasmas with the Fermi momentum close to $m_{e}c$, where $m_{e}$ is the mass of electron, and $c$ is the speed of light. The increase of the increment of instability with the growth of the spin polarization of plasmas is found., Comment: 9 Pages, 1 figure

The spin-electron-acoustic waves (sometimes called the spin-plasmons) can be found in degenerate electron gas if the spin-up electrons and spin down electrons move relatively each other. Here, we suggest relativistic hydrodynamics with the separate spin evolution which allows us to study linear and nonlinear spin-electron-acoustic waves, including the spin-electron-acoustic solitons. Presented hydrodynamic model is the corresponding generalization of the relativistic hydrodynamic model with the average reverse gamma factor evolution which consists of the equations for evolution of the following functions the partial concentrations (for spin-up electrons and spin down electrons), the partial velocity fields, the partial average reverse relativistic gamma factors, and the partial flux of the reverse relativistic gamma factors. We find that the relativistic effects decreases the phase velocity of spin-electron-acoustic waves. Numerical analysis of the changes of spectra of Langmuir wave, spin-electron-acoustic wave, and ion-acoustic wave under the change of the spin polarization of electrons is presented. It is demonstrated that spectra of Langmuir wave and spin-electron-acoustic wave getting closer to each other in the relativistic limit. Spin dependence of the amplitude and width of the relativistic spin-electron-acoustic soliton is demonstrated as well. Reformation of the bright soliton of potential of the electric field into the dark soliton under the influence of the relativistic effects is found., Comment: 13 pages, 8 figures

High-density low-temperature plasmas with degenerate species are considered in the limit of high Fermi velocities close to the speed of light. The small amplitude ion-acoustic solitons are studied in this regime. Presented analysis is based on the relativistic hydrodynamic model with the average reverse gamma factor evolution consists of the equations for evolution of the following functions the concentration, the velocity field, the average reverse relativistic gamma factor, and the flux of the reverse relativistic gamma factor, which are considered as main hydrodynamic variables. Justification of the suggested model via comparison of the hydrodynamic results with the result of application of the relativistic Vlasov kinetic equation is made in the linear approximation., Comment: 10 pages

The structure of novel hydrodynamic model of plasmas with the relativistic temperatures consisted of four equations for the material fields is presented for the regime of anisotropic pressure and other tensors describing the thermal effects. Presented model constructed of equation for evolution of the concentration, the velocity field, the average reverse relativistic $\gamma$ functor, and the flux of the reverse relativistic $\gamma$ functor, which are considered as main hydrodynamic variables. Four pressure-like tensors (two second rank tensors and one fourth rank tensor) describe the thermal effects. Among them we have the flux of the particle current and the current of the flux of the reverse relativistic $\gamma$ functor. The high-frequency excitations are considered analytically in order to trace the contribution of the anisotropy of pressure-like tensors in their spectra., Comment: 7 pages. arXiv admin note: text overlap with arXiv:2107.13603

Relativistic hydrodynamics of classic plasmas is derived from the microscopic model in the limit of ideal plasmas. The chain of equations is constructed step by step starting from the concentration evolution. It happens that the energy density and the momentum density do not appear at such approach, but new relativistic-hydrodynamic variables appear in the model. These variables has no nonrelativistic analogs, but they are reduced to the concentration, the particle current, the pressure (the flux of the particle current) if relativistic effects are dropped. These variables are reduced to functions of the concentration, the particle current, the pressure if the thermal velocities are dropped in compare with the relativistic velocity field. Final equations are presented in the monopole limit of the meanfield (the selfconsistent field) approximation. Hence, the contributions of the electric dipole moment, magnetic dipole moment, electric quadrupole moment, etc of the macroscopically infinitesimal element of volume appearing in derived equations are dropped., Comment: 13 pages

Generative adversarial networks (GANs) have an enormous potential impact on digital content creation, e.g., photo-realistic digital avatars, semantic content editing, and quality enhancement of speech and images. However, the performance of modern GANs comes together with massive amounts of computations performed during the inference and high energy consumption. That complicates, or even makes impossible, their deployment on edge devices. The problem can be reduced with quantization -- a neural network compression technique that facilitates hardware-friendly inference by replacing floating-point computations with low-bit integer ones. While quantization is well established for discriminative models, the performance of modern quantization techniques in application to GANs remains unclear. GANs generate content of a more complex structure than discriminative models, and thus quantization of GANs is significantly more challenging. To tackle this problem, we perform an extensive experimental study of state-of-art quantization techniques on three diverse GAN architectures, namely StyleGAN, Self-Attention GAN, and CycleGAN. As a result, we discovered practical recipes that allowed us to successfully quantize these models for inference with 4/8-bit weights and 8-bit activations while preserving the quality of the original full-precision models.

The Alfvenic waves and fast magneto-sound in the relativistically hot plasmas are considered. This study is based on the novel hydrodynamic model of plasmas with the relativistic temperatures consisted of four equations for the material fields: the concentration and the velocity field \emph{and} the average reverse relativistic $\gamma$ functor and the flux of the reverse relativistic $\gamma$ functor. Three temperature regimes giving considerably different behavior of the spectrum of Alfvenic waves are found. Four temperature regimes are obtained for the fast magneto-sound. All these regimes show considerable variations from the nonrelativistic regime. Dispersion equations for the electromagnetic transverse wave propagating parallel to the external magnetic field are found analytically. Their small frequency solutions are analyzed numerically., Comment: 9 pages, 9 figures

Due to the many unique transport properties of Weyl semimetals, they are promising materials for modern electronics. We investigate the electrons in the strong coupling approximation near Weyl points based on their representation as massless Weyl fermions. We have constructed a new fluid model based on the many-particle quantum hydrodynamics method to describe the behavior of electrons gas with different chirality near Weyl points in the low-energy limit in the external electromagnetic fields, based on the many-particle Weyl equation and many-particle wave function. The derived system of equations forms a closed apparatus for describing the dynamics of the electron current, spin density and spin current density. Based on the proposed model, we considered small perturbations in the Weyl fermion system in an external uniform magnetic field and predicted the new type of eigenwaves in the systems of the electrons near the Weyl points.

The novel hydrodynamic model of plasmas with the relativistic temperatures consisted of four equations for the material fields: the concentration and the velocity field \emph{and} the average reverse relativistic $\gamma$ functor and the flux of the reverse relativistic $\gamma$ functor is applied to study high-frequency part of spectrum of electromagnetic waves propagating perpendicular to the external magnetic field. The thermal effects considered for the temperatures close to the rest energy of electrons considerably change the dispersion equation in compare with the nonrelativistic temperatures. Analytical analysis of the changes is presented., Comment: 5 pages

The high-frequency part of spectrum of electromagnetic waves propagating parallel to the external magnetic field is considered for the macroscopically motionless plasmas with the relativistic temperatures $T\sim m_{e}c^{2}$, where $m_{e}$ is the mass of electron, $c$ is the speed of light. The analysis is based on the novel hydrodynamic model based on four equations for the material fields which can be combined in two four vectors. These material fields are the concentration and the velocity field \emph{and} the average reverse relativistic $\gamma$ functor and the flux of the reverse relativistic $\gamma$ functor. In the nonrelativistic regime we have three waves (the ions are assumed to be motionless). Strong thermal effects lead to a coefficient in front of cyclotron frequency which decreases the effective contribution of the cyclotron frequency. At $T=0.1m_{e}c^{2}$ we have a decrease of area of existence of fast magneto-sound wave from the area of the large frequencies. While the area of existence of extraordinary waves becomes larger towards smaller frequencies. The strong magnetic field limit $\mid\Omega_{e}\mid > \omega_{Le}$ additional wave appears with frequency below thermally decreased cyclotron frequency, where $\mid\Omega_{e}\mid$ is the electron cyclotron frequency, and $\omega_{Le}$ is the Langmuir frequency. Further increase of temperature leads to the disappearance of fast magneto-sound wave and to the considerable increase of area of existence of extraordinary towards smaller frequencies., Comment: 8 pages, 3 figures

Novel structure for relativistic hydrodynamics of classic plasmas is derived following the microscopic dynamics of charged particles. The derivation is started from the microscopic definition of concentration. Obviously, the concentration evolution leads to the continuity equation and gives the definition of particle current. Introducing no arbitrary functions, we consider the evolution of current (which does not coincide with the momentum density). It leads to a set of new function which, to the best of our knowledge, have not been consider in the literature earlier. One of these functions is the average reverse relativistic (gamma) factor. Its current is also considered as one of basic functions. Evolution of new functions appears via the concentration and particle current so the set of equations partially closes itself. Other functions are presented as functions of basic function as a part of truncation presiger. Two pairs of chosen functions construct two four vectors. Evolution of these four vectors leads to appearance of two four tensors which are considered instead of the energy-momentum tensor. The Langmuir waves are considered within the suggested model., Comment: 8 pages, 1 figure

A minimal coupling quantum hydrodynamic model of spin-1/2 fermions at the full spin polarization corresponding to a nonlinear Schrodinger equation is considered. The nonlinearity is primarily caused by the Fermi pressure. It provides an effective repulsion between fermions. However, there is the additional contribution of the short-range interaction appearing in the third order by the interaction radius. It leads to the modification of the pressure contribution. Solitons are considered for the infinite medium with no restriction on the amplitude of the wave. The Fermi pressure leads to the soliton in form of the area of decreased concentration. However, the center of solution corresponding to the area of minimal concentration has nonzero value of concentration. Therefore, the grey soliton is found. Soliton exist if the speed of its propagation is below the Fermi velocity., Comment: 6 pages, 4 figures

Quantum hydrodynamic of skyrmions in spinor ultracold bosons at the finite temperature is described. The limit regime of BEC appearing at the zero temperature is discussed either. The skyrmions are found as the solution of the spin evolution equation for the ferromagnetic phase of spin-1 ultracold bosons. It is demonstrated that the quantum part of the spin current gives major contribution in the formation of the skyrmions. The interplay between the quantum (spin) vorticity and the classic vorticity is considered for the finite temperatures. Bosons are presented as two fluids associated with the Bose-Einstein condensate and the normal fluid. All effects are considered for the ferromagnetic phase., Comment: 10 pages

Finite temperature hydrodynamic model is derived for the spin-1 ultracold bosons by the many-particle quantum hydrodynamic method. It is presented as the two fluid model of the BEC and normal fluid. The linear and quadratic Zeeman effects are included. Scalar and spin-spin like short-range interactions are considered in the first order by the interaction radius. It is also represented as the set of two nonlinear Pauli equations. The spectrum of the bulk collective excitations is considered for the ferromagnetic phase in the small temperature limit. The spin wave is not affected by the presence of the small temperature in the described minimal coupling model, where the thermal part of the spin-current of the normal fluid is neglected. The two sound waves are affected by the spin evolution in the same way as the change of spectrum of the single sound wave in BEC, where speed of sound is proportional to $g_{1}+g_{2}$ with $g_{i}$ are the interaction constants., Comment: 12 pages

Ultracold Bose atoms is the physical system, where the quantum and nonlinear phenomena play crucial role. Ultracold bosons are considered at the small finite temperatures. Bosons are considered as two different fluids: Bose-Einstein condensate and normal fluid (the thermal component). An extended hydrodynamic model is obtained for both fluids, where the pressure evolution equations and the pressure flux third rank tensor evolution equations are considered along with the continuity and Euler equations. It is found that the pressure evolution equation contains zero contribution of the short-range interaction. The pressure flux evolution equation contains the interaction which gives the quantum fluctuations in the zero temperature limit. Here, we obtain its generalization for the finite temperature. The contribution of interaction in the pressure flux evolution equation which goes to zero in the zero temperature limit is found. The model is obtained via the straightforward derivation from the microscopic many-particle Schrodinger equation in the coordinate representation., Comment: 15 pages

Solitons in the extended hydrodynamic model of the dipolar Bose-Einstein condensate with quantum fluctuations are considered. This model includes the continuity equation for the scalar field of concentration, the Euler equation for the vector field of velocity, the pressure evolution equation for the second rank tensor of pressure, and the evolution equation for the third rank tensor. Large amplitude soliton solution caused by the dipolar part of quantum fluctuations is found. It appears as the bright soliton. Hence, it is the area of compression of the number of particles. Moreover, it exists for the repulsive short-range interaction., Comment: 9 pages, 4 figures

Several hydrodynamic models the atomic Bose-Einstein condensate beyond the mean-field approximation are discussed together from one point of view. All these models are derived from microscopic quantum description. The derivation is made within the many-particle quantum hydrodynamics method suggested by L. Kuz'menkov. The derivation is demonstrated and discussed for the mean-field regime revealing the Gross-Pitaevskii equation as the simplest illustration. It appears in the first order by the interaction radius. Generalization of the hydrodynamic Euler equation obtained in the third order by the interaction radius are discussed. It includes the contribution of the isotropic short-range interaction presented by the third space derivative of the square of concentration. The Euler equation also includes the contribution of the anisotropic part of the short-range interaction proportional to the second order spherical function. Systematic account of the quantum fluctuations in terms of the many-particle quantum hydrodynamics method requires the extension of the set of hydrodynamic equations from the couple continuity and Euler equations to the set of four equations which also includes the pressure evolution equation and the evolution equation for the third rank analog of pressure. The pressure evolution equation contains no interaction contribution in the first order by the interaction radius. The source of the quantum fluctuations is in the interaction caused term in the third rank tensor evolution equation which is obtained in the first order by the interaction radius., Comment: 10 pages

If we study the quantum effects in plasmas in terms of traditional hydrodynamics via the continuity and Euler equations we find the quantum Bohm potential and the force of spin-spin interaction. However, if we extend the set hydrodynamic equations beyond the 13-moments approximation, and include the third rank tensor evolution equation along with the pressure evolution equation, we obtain the quantum corrections to the Coulomb interaction. It is found in contrast with the fact that hydrodynamic equations for the higher rank tensors do not contain interaction in the classic plasmas studied in the selfconsistent (meanfield) approximation. Therefore, we present the quantum hydrodynamic model, where the quantum effects are studied beyond the quantum Bohm potential. Developed model is considered in two regimes: all electrons in plasmas are considered as the single fluid, and the separate spin evolution regime, where electrons with different spin projections are considered as two different fluids. To illustrate the fundamental meaning of found quantum effects we demonstrate their contribution in the spectrum of the Langmuir waves and the spin-electron-acoustic waves. It is worth to mention that the application of the pressure evolution equation ensures that the contribution of pressure in the Langmuir wave spectrum is proportional to $(3/5)v_{Fe}^{2}$, unlike $(1/3)v_{Fe}^{2}$ appearing from hydrodynamics based on the continuity and Euler equations, where $v_{Fe}$ is the Fermi velocity. Same correction corresponds on other plasmas phenomena like the speed of sound for spin-electron-acoustic waves. Moreover, it is found that novel quantum effects provide the novel wave solutions., Comment: 5+3 pages

Traditional quantum hydrodynamics of Bose-Einstein condensates (BECs) is restricted by the continuity and Euler equations. It corresponds to the well-known Gross-Pitaevskii equation. However, the quantum Bohm potential, which is a part of the momentum flux, has a nontrivial part with can evolve under the quantum fluctuations. To cover this phenomenon in terms of hydrodynamic methods we need to derive equations for the momentum flux, and the third rank tensor. In all equations we consider the main contribution of the short-range interaction (SRI) in the first order by the interaction radius. Derived hydrodynamics consists of four hydrodynamic equations. The third moment evolution equation contains interaction leading to the quantum fluctuations. It includes new interaction constant. The Gross-Pitaevskii interaction constant is the integral of potential, but the second interaction constant is the integral of second derivative of potential. If we have dipolar BECs we deal with a long-range interaction. Its contribution is proportional to the potential of dipole-dipole interaction (DDI). The Euler equation contains the derivative of the potential. The third rank tensor evolution equation contains the third derivative of the potential. The quantum fluctuations lead to existence of the second wave solution. Moreover, the quantum fluctuations introduce the instability of BECs. If the DDI is attractive, but being smaller then the repulsive SRI presented by the first interaction constant, there is the long-wavelength instability. For the repulsive DDI these is more complex picture. There is the small area with the long-wavelength instability which transits into stability interval, where two waves exist. There is the short-wavelength instability as well. These results are found for the DDI strength comparable with the Gross-Pitaevskii SRI., Comment: 6+3 pages, 3+2 figures

Repulsive Bose-Einstein condensate, where the short-range interaction is included up to the third order by the interaction radius, demonstrates existence of a bright soliton in a narrow interval of parameters. This soliton is studied here for the boson-fermion mixture, where spin-1/2 fermions are consider in the regime of full spin polarization. Influence of fermions via the boson-fermion interaction is considered up to the third order by the interaction radius. Fermions themselves are considered by hydrodynamic model including the pressure evolution equation. Interaction between fermions is considered. The first order by the interaction radius gives zero contribution in the Euler equation and the pressure evolution equation, but the third order by the interaction radius provides nonzero contributions in both equations. Repulsive (attractive) boson-fermion interaction leads to the bright (dark) fermionic soliton., Comment: 13 pages, 8 figures

A possibility of the hydrodynamic description of ultracold fermions via the microscopic derivation of the model is described. Differently truncated hydrodynamic models are derived and compared. All models are based on the microscopic many-particle Schr\"{o}dinger equation. Minimal coupling model based on the continuity and Euler equations are considered. The extended hydrodynamic model including the independent dynamics of the momentum flux (the pressure evolution) is derived. Influence of the spin polarization is described. The short-range interaction is considered in the isotropic limit. The interaction is considered up to the third order by the interaction radius. Therefore, the single fluid model of spin-1/2 fermions and the two fluid model of spin-1/2 fermions are under consideration in this paper. Spectra of bulk collective excitations are derived and compared in terms of different models., Comment: 27 pages

Usually, hydrodynamic equations are restricted by the continuity and Euler equations. However, the account of the higher moments of the distribution function gives better description of the kinetic properties. Therefore, the pressure tensor evolution equation (PTEE) is derived for spin polarized degenerate fermions. Moreover, it is found that the pressure tensor enters the interaction term generalizing the p-wave interaction in the Euler equation. Hence, the PTEE allows to give a more accurate description of the interaction in Euler equation. Next, the interaction is calculated for the PTEE. The developed model is applied to the small amplitude bulk collective excitations in homogeneous and trapped fermions in order to suggest the methods of experimental measurement of the interaction constant of polarized fermions. It is demonstrated that the anisotropy in the momentum space revealing in the difference of the pressures in the anisotropy direction and the perpendicular directions leads to a method of detection of the interaction constant., Comment: 6 pages, 3 figures

Skyrmions dynamics in the approximation of point-particle skyrmions is considered in the multiferroic insulators, where the spiral magnetic structure is accompanied by finite electric dipole moment. The skyrmion motion is studied in the gradients of perpendicular magnetic and electric fields. The nonuniform magnetic field with a fixed gradient magnitude leads to the spiral motion, where skyrmion circulates in the plane perpendicular to the direction of magnetic field. The frequency of circulation is fixed by the derivative of the external magnetic field and the magnitude of the dipole moment. Application of additional electric field which perpendicular to the magnetic field, but their gradients have same direction leads to the drift motion of skyrmions resulting in the magneto-dipolar Hall effect. Hydrodynamics of the gas of interacting skyrmions in crossed nonuniform electric and magnetic fields shows the new type of hydrodynamical instability caused by the drift motion. Three regimes of instability are described., Comment: 6 pages, 1 figure

The quantum hydrodynamic model is developed for the axial symmetric anisotropic short-range interaction. The quantum stress tensor presents the interaction. It is derived up to the third order by the interaction radius. The first order by the interaction radius contains the isotropic part only. It leads to the interaction in the Gross-Pitaevskii approximation. Terms existing in the third order by the interaction radius are caused by the isotropic and nonisotropic parts of the interaction. Each of them introduces the interaction constant. Therefore, three interaction constants are involved in the model. Atoms, except the alkali and alkali-earth atoms, can have anisotropic potential of interaction, particularly it is demonstrated for the lanthanides. The short-wavelength instability caused by the nonlocal terms appears in the Bogoliubov spectrum. Conditions for the stable and unstable behaviour are described. Bright solitons in the repulsive BEC are studied under influence of the anisotropic short-range interaction in the BEC of one species. Area of existence of this bright solitons corresponds to the area of the instability of the Bogoliubov spectrum. Approximate reduction of the nonlocal nonlinearity to the quintic nonlinearity at the description of the bright solitons is demonstrated either., Comment: 13 pages, 5 figures

The quantum hydrodynamic model of the electrostatic waves in the two parallel layers of two dimensional electron gases (2DEGs) is developed. It is considered for two regimes: classic regime and quantum regime with the separate spin evolution. Two Langmuir-like waves are found in classic case which have an interference-like pattern in the frequency dependence on concentration $\omega^{2}\sim(n_{01}+n_{02}\pm2\sqrt{n_{01}n_{02}})$. They appear instead of two 2D Langmuir waves in noninteracting 2DEGs. The spectrum of four waves is found in the quantum regime. Two extra waves are related to the separate spin evolution and associated to the spin-electron acoustic waves. The influence of the quantum Bohm potential is considered either., Comment: 9 pages, 14 figures

The separate spin evolution (SSE) of electrons causes the existence of the spin-electron acoustic wave. Extraordinary spin-electron acoustic waves (SEAWs) propagating perpendicular to the external magnetic field have large contribution of the transverse electric field. Its spectrum has been studied in the quasi-classical limit at the consideration of the separate spin evolution. The spin-spin interaction and the quantum Bohm potential give contribution in the spectrum extraordinary SEAW. This contribution is studied in this paper. Moreover, it is demonstrated that the spin-spin interaction leads to the existence of the extraordinary SEAWs if the SSE is neglected. The hybridization of the extraordinary SEAW and the lower extraordinary wave in the regime, where the cyclotron frequency is larger then the Langmuir frequency is studied either., Comment: 8 pages, 8 figures

Influence of the exchange interaction on the properties of the spin-electron acoustic waves at the oblique propagation of waves relatively to the external magnetic field in the magnetically ordered metals is studied. The spectra of the Langmuir wave and the Trivelpiece-Gould wave are also considered. It is well-known that there are two branches of spectrum of the spin-electron acoustic waves in this regime. Change their properties under influence of the exchange interaction is studied. The quantum Bohm potential is included either. The exchange interaction and quantum Bohm potential gives opposite contributions, but they do not compensate each other since they have different dependence on the wave vector. This competition creates a non-monotonical behavior of the Trivelpiece-Gould wave spectrum. The concavity changes in the monotonic spectra of the Langmuir wave and the SEAWs are found., Comment: 8 pages, 8 figures

Oblique propagation of the spin-electron acoustic waves in degenerate magnetized plasmas is considered in terms of quantum kinetics with the separate spin evolution, where the spin-up electrons and the spin-down electrons are considered as two different species with different equilibrium distributions. It is considered in the electrostatic limit. Corresponding dispersion equation is derived. Analytical analysis of the dispersion equation is performed in the long-wavelength limit to find an approximate dispersion equation describing the spin-electron acoustic wave. The approximate dispersion equation is solved numerically. Real and imaginary parts of the spin-electron acoustic wave frequency are calculated for different values of the parameters describing the system. It is found that the increase of angle between direction of wave propagation and the external magnetic field reduces the real and imaginary parts of spin-electron acoustic wave frequency. The increase of the spin polarization decreases the real and imaginary parts of frequency either. The imaginary part of frequency has nonmonotonic dependence on the wave vector which shows a single maximum. The imaginary part of frequency is small in compare with the real part for all parameters in the area of applicability of the obtained dispersion equation., Comment: 8 pages, 7 figures