Static properties of a warm dense uniform electron gas

Copyright 2021 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in J. Ara, Ll. Coloma, and I. M. Tkachenko , "Static properties of a warm dense uniform electron gas", Physics of Plasmas 28, 112704 (2021) https://doi.org/10.1063/5.0062259[EN] We show how the static dielectric function and other static characteristics of dense warm charged Fermi liquids can be obtained exclusively from the system static structure factor. The non-perturbative self-consistent method of moments is employed to extend onto quantum fluids, a similar reduction stemming from the fluctuation-dissipation theorem and other exact relations for classical one-component plasmas. The results are compared to and complement the numerical data obtained recently by the path-integral Monte Carlo method. Alternative theoretical approaches are discussed and employed as well.I.M.T. is grateful to M. Bonitz and T. Dornheim for several valuable discussions. The authors appreciate that M. Bonitz and T. Dornheim provided accurate path integral Monte Carlo simulation results. I.M.T. also acknowledges fruitful discussions with Yu. V. Arkhipov and L. Conde and the financial support provided by the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan (Project No. AP09260349).Ara-Bernad, J.; Coloma, L.; Tkachenko Gorski, IM. (2021). Static properties of a warm dense uniform electron gas. Physics of Plasmas. 28(11):1-17. https://doi.org/10.1063/5.0062259117281

Self-consistent relaxation theory of collective ion dynamics in Yukawa one-component plasmas under intermediate screening regimes

[EN] The self-consistent relaxation theory is employed to describe the collective ion dynamics in strongly coupled Yukawa classical one-component plasmas. The theory is applied to equilibrium states corresponding to intermediate screening regimes with appropriate values of the structure and coupling parameters. The information about the structure (the radial distribution function and the static structure factor) and the thermodynamics of the system are sufficient to describe collective dynamics over a wide range of spatial scales, namely, from the extended hydrodynamic to the microscopic dynamics scale. The main experimentally measurable characteristics of the equilibrium collective dynamics of ions-the spectrum of the dynamic structure factor, the dispersion parameters, the speed of sound, and the sound attenuation-are determined within the framework of the theory without using any adjustable parameters. The results demonstrate agreement with molecular dynamics simulations. Thus a direct realization is presented of the key idea of statistical mechanics: for the theoretical description of the collective particle dynamics in equilibrium fluids it is sufficient to know the interparticle interaction potential and the structural characteristics. Comparison with alternative or complementary theoretical approaches is provided.This work was supported by the Russian Science Foundation (Project No. 19-12-00022). I.M.T. acknowledges the financial support provided by the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan (Project No. AP09260349). A.V.M. acknowledges the Theoretical Physics and Mathematics Advancement Foundation ¿BASIS¿ (Project No. 20-1-2-38-1) for supporting the computational part of this work. The authors are grateful to R. M. Khusnutdinoff and B. N. Galimzyanov for discussion of the results of molecular dynamics simulations.Mokshin, AV.; Fairushin, II.; Tkachenko Gorski, IM. (2022). Self-consistent relaxation theory of collective ion dynamics in Yukawa one-component plasmas under intermediate screening regimes. Physical review. E, Statistical, nonlinear, and soft matter physics. 105(2):1-7. https://doi.org/10.1103/PhysRevE.105.02520417105

Stopping of charged particles in dense one-component plasmas

Arkhipov, YV.; Askaruly, A.; Ashikbayeva, A.; Dubovtsev, D.; Syzganbayeva, S.; Tkachenko Gorski, IM. (2018). Stopping of charged particles in dense one-component plasmas. Recent Contribution to Physics. 65(2):51-57. http://hdl.handle.net/10251/133780S515765

Analysis of methods for calculating the static characteristics of dense Coulomb systems

[EN] In this paper, various methods for calculating static characteristics of plasma, such as HNC, MHNC, VMHNC, Percus-Yevik and analytical models were analyzed to satisfy a mathematical condition. Structural characteristics of a one-component plasma were reconstructed in a wide range of coupling parameters within the most requested various modern methods (HNC, MHNC, VMHNC, Percus-Yevik, and analytical models). All these methods were analyzed to fulfill the fundamental Cauchy ¿ Schwartz mathematical inequality. As a result a HNC method with the empirical expression of the bridge function and one of the recent methods for obtaining a structural factor based on a parameterized formula does not satisfy the inequality. The other methods for calculating static characteristics listed above beside the stated ones satisfy the condition. For the general analysis of a method, functional dependence was obtained expressing the Cauchy-Schwartz inequality. This dependence includes the frequency moments, which are defined within the framework of the method of moments. To satisfy the inequality, this relationship must be strictly positive. For each considered method of obtaining static structural characteristics, this relationship was calculated and analyzed. As a result, it was found that a number of methods do not satisfy the Cauchy-Schwartz inequality.Arkhipov, YV.; Askaruly, A.; Ashikbayeva, A.; Davletov, A.; Dubovtsev, D.; Santybayev, K.; Tkachenko Gorski, IM. (2018). Analysis of methods for calculating the static characteristics of dense Coulomb systems. Recent Contribution to Physics. 67(4):20-32. http://hdl.handle.net/10251/133778S203267

Local moment problem

The work is devoted to the local moment problem, which consists in finding of non-decreasing functions on the real axis having given first 2n+1; n = 0,1,2,...; power moments on the whole axis and also 2m+1 first power moments on a certain finite axis interval. Considering the local moment problem as a combination of the Hausdorff and Hamburger truncated moment problems we obtain the conditions of its solvability and describe the class of its solutions with minimal number of growth points if the problem is solvable.Adamyan, V.; Tkachenko Gorski, IM. (2014). Local moment problem. Proceedings in Applied Mathematics and Mechanics. 14(1):981-982. doi:10.1002/pamm.201410471S981982141N.I. Akhiezer The classical moment problem and some related questions in analysis, Hafner Publishing N.Y. Company (1965).M.G. Krein Nudel'man A.A., The Markov moment problem and extremal problems, Translation of Mathematical Monographs AMS, 50 (1977).V. Adamyan I. Tkachenko Solution of the Truncated Matrix Hamburger Moment Problem According to M.G. Krein. Operator Theory: Advances and Applications, vol. 118(Proceedings of the Mark Krein International Conference on Operator Theory and Applications, vol.II, Operator Theory and Related Topics), Birkhäuser Verlag Basel, (2000), 32 - 51.V. Adamyan I. Tkachenko M. Urrea Solution of the Stieltjes truncated moment problem, J. Applied Analysis, vol. 9, N.1 (2003) 57-74.V. Adamyan I. Tkachenko Solution of the Stieltjes Truncated Matrix Moment Problem, Opuscula Mathematica, v. 25/1 (2005), 5-24.V. Adamyan I. Tkachenko General Solution of the Stieltjes Truncated Matrix Moment Problem, Operator Theory: Advances and Applications v. 163 (2005), 1- 22

FUNDAMENTOS MATEMÁTICOS DE LA INGENIERÍA QUÍMICA. ECUACIONES DIFERENCIALES Y TEMAS COMPLEMENTARIOS

Este libro recoge la experiencia docente de los autores en diversas universidades durante varios años. Por un lado, presenta temas obligatorios y tradicionales como son Álgebra Lineal, Ecuaciones Diferenciales Ordinarias y EDDP; por otro lado, se han incluido unos capítulos que exponen la Teoría de Funciones de Variable Compleja con las transformadas de Fourier y Laplace, Espacios Vectoriales, Método de Funciones de Green y, todo ello, se complementa con algunos problemas representativos de Mecánica Cuántica. Con este libro, el lector podrá reforzar sus estudios sobre matemáticas para Ingeniería Química y Química Física, así como afrontar otros problemas que pueden surgir en su ejercicio profesionalTkachenko Gorski, IM.; Ferrer Villanueva, JR. (2019). FUNDAMENTOS MATEMÁTICOS DE LA INGENIERÍA QUÍMICA. ECUACIONES DIFERENCIALES Y TEMAS COMPLEMENTARIOS. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/118515EDITORIA

Dust acoustic waves in complex plasmas at elevated pressure

The bi-Yukawa effective interaction potential with different screening constants is employed to calculate dust static correlation functions in the hyper-netted chain approximation and to generalize the theory of dust acoustic waves within the non-perturbative moment approach complemented by hydrodynamic considerations. For the bi-Yukawa interaction potential the sound speed becomes significantly wavenumber-dependent, an additional soft diffusion-like mode is predicted, and the static dielectric function is shown to take negative values. The results can be applied to non-equilibrium dusty plasmas at elevated pressure.The work was supported by the Spanish Ministerio de Ciencia e Innovacion under Grant No. ENE2010-21116-C02-02 and the Ministry of Education and Science of the Russian Federation under Grants Nos. 02.740.11.0569, 14.740.11.0159 and NSh-3239.2010.2. I.M.T. is grateful to the Polytechnic University of Valencia for the sabbatical leave he was granted. We thank Vit. Rerikh, B. Klumov and L. Conde for useful discussions.Filippov, AV.; Starostin, AN.; Tkachenko Gorski, IM.; Fortov, VE. (2011). Dust acoustic waves in complex plasmas at elevated pressure. Physics Letters A. 376(1):31-38. https://doi.org/10.1016/j.physleta.2011.10.030S3138376

Electrostatic interactions and stability of dusty plasmas and the multicomponent Ornstein-Zernike equation

[EN] Using the Ornstein-Zernike integral fluid equation for multi-component plasma, the dielectric properties and thermodynamical stability of dusty plasmas are studied. For the most non-ideal dust plasma subsystem, a transition to the one-component approximation is carried out. It is shown that the effective pseudopotential for determining the correlation functions in the selected subsystem should not include the contribution of this subsystem to the screening constant but also take into account the condition of total plasma quasineutrality. It is demonstrated that when the coupling parameter of the dust subsystem is smaller than unity, Gamma(00) 1, the static dielectric function in the long wavelength domain becomes negative, and this domain expands when Gamma(00) increases. This leads to the appearance of attraction of particles with charges of the same sign and repulsion of particles with charges of the opposite sign. In this case, both the total pressure and the isothermal compressibility in the entire studied range of the coupling parameter Gamma(00) 2 is thermodynamically unstable.This study was developed within Project No. 16-12-10424 supported by the grant from the Russian Science Foundation, and the numerical simulations were carried out as a part of the State assignment financed by the Ministry of Science and Higher Education of the Russian Federation (Project No. 0038-2019-0005).Tkachenko Gorski, IM.; Filippov, A.; Fortov, VE.; Reshetniak, V.; Starostin, A. (2020). Electrostatic interactions and stability of dusty plasmas and the multicomponent Ornstein-Zernike equation. AIP Advances. 10(4):1-14. https://doi.org/10.1063/1.514490111410

Norms of positive definite toeplitz matrices and detection of almost periodic components in random signals

For positive definite Toeplitz matrices generated by trigonometric moments of a non-negative measure we note that the Hilbert-Schmidt norm and the maximal eigenvalue satisfy certain limiting relations. Analogous relations hold for positive definite integral operators with difference kernels. The obtained relations are used in order to detect hidden almost periodic components in random signals.The financial support of the Polytechnic University of Valencia is gratefully acknowledged.Adamyan, V.; Iserte Vilar, JL.; Tkachenko Gorski, IM.; Verdú Martín, GJ. (2014). Norms of positive definite toeplitz matrices and detection of almost periodic components in random signals. Operators and Matrices. 8(3):861-875. doi:10.7153/oam-08-48S8618758

Energy loss of relativistic projectiles in non-ideal electron liquids

[EN] The energy loss of relativistic projectiles in collisional one-component plasmas is analyzed within the method of moments. Both the canonical and non-canonical solutions of the Hamburger moment problem corresponding to five convergent power frequency moments of the electron plasma loss function are employed with the static, purely imaginary, Nevanlinna parameter with the imaginary part iqual to the collision frequency calculated within the Green-Kubo formalism in terms of static structure factors evaluated in the HNC approximation using the Deutsch effective potential.Thus we take into account the dissipation processes in the plasma. It is pointed out that the correlations only slightly influence the deviation of the stopping power with the relativistic corrections taken into account from the classical Bethe-Bohr-Larkin asymptotic form.The financial support of the Spanish Ministerio de Educación y Ciencia Project # ENE2010-21116-C02-02 and the Ministry of education and science of the Republic of Kazakhstan projects #1128/GF, 1129/GF, 1099/GF are gratefully acknowledged. IMT acknowledges also the hospitality of the al-Farabi Kazakh National UniversityArkhipov, YV.; Ashikbayeva, A.; Askaruly, A.; Davletov, A.; Palací, D.; Tkachenko Gorski, IM. (2013). Energy loss of relativistic projectiles in non-ideal electron liquids. International Journal of Mathematics and Physics. 4(1):50-55. http://hdl.handle.net/10251/15511450554