# Igor M. TkachenkoUniversitat Politècnica de València | UPV · Department of Applied Mathematics

Igor M. Tkachenko

PhD, Dr. Sc., Dr. H.C. RAS

## About

126

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Introduction

Working on static and dynamic properties of strongly coupled plasmas, both classical and quantum, and warm-dense matter, employing the self-consistent method of moments. In 3d and 2d cases. Study dynamic properties of Dirac massless electrons in the RPA and beyond.

Additional affiliations

April 1987 - July 1987

## Publications

Publications (126)

The density-density dynamic structure factor and the eigenmodes of density fluctuations in the uniform liquid $^3$He are studied using a novel non-perturbative approach. The introduced self-consistent method of moments invokes up to nine sum rules and other exact relations involving the spectral density, the two-parameter Shannon information entrop...

Collective processes in a quasi-classical electron gas are investigated within the frame- work of the interpolational self-consistent method of moments, which makes it possible to express the dispersion and decrement of plasma waves, and the dynamic structural factor of the system exclusively in terms of its static structural factor so that five su...

We apply a novel 9-moment variational version of the self-consistent non-perturbative method of moments to study how the temperature affects the dynamic response of the electron gas in thermodynamic equilibrium. The theoretical results are obtained with the only input being the static structure factor. Comparison is carried out with the data obtain...

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 r...

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 r...

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 a...

The dynamic structure factor and other dynamic characteristics of strongly coupled one-component plasmas have been studied [Yu. V. Arkhipov et al., Phys. Rev. Lett. 119, 045001 (2017)] using the self-consistent version of the method of moments. Within any version of the latter, the system dielectric function satisfies all involved sum rules and oth...

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 correlat...

The electrostatic interaction between charged particles in a dusty plasma has been studied using the Ornstein—Zernike integral equation for a multicomponent plasma. The transition to the one-component approximation has been performed for the nonideal plasma subsystem. It has been shown that the interaction between charged plasma particles at the co...

The stopping power of dense electron plasmas is determined using a simplified version of the method of moments based on some interpolation formulas for the sum rules of the loss function. The energy losses of ions are evaluated with various projectile charges moving in a plasma at different values of the coupling and degeneracy parameters. The loss...

The algorithm suggested in [30], which permits to determine dynamic characteristics of strongly coupled one-component plasmas without any data input from simulations or direct experiments, is extended to a partially degenerate two-dimensional electron gas. The approach is based on the classical theory of moments and other exact relations satisfied...

The aim of the present study is to determine the impact the finite size of dust particles has on the static and dynamic characteristics of the dust component of a plasma. Taking into account both the finite dimensions of dust grains and the plasma screening, a model expression is chosen for the interdust interaction potential. The static structure...

Grounded on the premise that dust particles are charged hard balls, the analysis in Davletov et al. ( Contrib. Plasma Phys. , vol. 56, 2016, 308) provides an original pseudopotential model of intergrain interaction in complex (dusty) plasmas. This accurate model is engaged herein to consistently treat the finite-size effects from the process of dus...

Several sum rules and other exact relations are employed to determine both the static and the dynamic properties of strongly coupled, partially and completely degenerate one‐component plasmas. Emphasis is placed on the electron gas, both at zero and finite temperatures. The procedure is based on the self‐consistent method of moments, recently devel...

Dynamic characteristics of strongly coupled classical one-component Coulomb and Yukawa plasmas are obtained within the nonperturbative model-free moment approach without any data input from simulations so that the dynamic structure factor (DSF) satisfies the first three nonvanishing sum rules automatically. The DSF, dispersion, decay, sound speed,...

The linear density response formalism is used to analytically obtain an effective pairwise interaction potential of charged particles that simultaneously takes into account quantum mechanical and quantum statistical effects in weakly and moderately non-ideal plasmas at thermal equilibrium. The static dielectric function is obtained by interpolating...

The problem of calculation of the electric charge of dust particles in a plasma is considered from different points of view. At first the charging of polarizable dust particles is studied within the orbital motion limited approach. Secondly, the plasma electrodynamics is applied to show that the electric charge of a dust particle is determined by t...

The dynamic structure factor of dense two-component plasmas is studied within the method of moments. A new model for the Nevanlinna parameter function is suggested. Our results on the dynamic structure factor satisfy the sum rules and other exact relations automatically, independently of the choice of a mathematically consistent model of the latter...

The fulfilment of sum rules for the loss function which is determined using different models of the dielectric function (DF): the random phase approximation (RPA), Mermin, and extended models of RPA and Mermin is investigated1. In the extended models the dynamic collision frequency is used, which is calculated according to computer simulations and...

The dense plasma dynamic collision frequency is modeled by the first two terms of its asymptotic expansion at high frequencies and its values at a few interpolation points on the real axis. This makes the dynamic collision frequency a non-rational function whose extension onto the upper half-plane of the complex frequency is holomorphic with a non-...

DOI:https://doi.org/10.1103/PhysRevE.91.019903

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, 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 truncate...

Mathematical, particularly, asymptotic properties of the random-phase approximation, Mermin approximation, and extended Mermin-type approximation of the coupled plasma dielectric function are analyzed within the method of moments. These models are generalized for two-component plasmas. Some drawbacks and advantages of the above models are pointed o...

For positive definite Toeplitz matrices Q(N) = (b(j - k))(j,k=0)(N-1) generated by trigonometric moments b(j) of a non-negative measure d sigma (theta), theta is an element of [-pi, pi], we note that the Hilbert-Schmidt norm parallel to Q(N)parallel to 2 and the maximal eigenvalue lambda(m)(N) satisfy the following relations

We report on a development of an alternative method of HED plasma diagnostics using the ideas of the method of moments [I.M. Tkachenko, J. Ortner, and J. Alcober, J. de Physique IV 10, 195 (2000)]. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The present paper is devoted to the {\it local moment problem}, which
consists in finding of non-decreasing functions on the real axis having given
first $2n+1, \; n\geq 0,$ 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 an...

Relativistic and correlation contributions to the polarizational energy
losses of heavy projectiles moving in dense two-component plasmas are
analyzed within the method of moments that allows one to reconstruct the
Lindhard loss function from its three independently known power
frequency moments. The techniques employed result in a thorough
separat...

Simulation data on hydrogen-like plasmas, modelled with the Kelbg pseudopotential, are treated within the classical theory of moments. The possibility is analyzed for the model inverse dielectric function to satisfy five convergent sum rules and other exact relations. The sum rules are the power frequency moments of the loss function and the latter...

The static dielectric function and dust acoustic waves are considered of non-equilibrium dusty plasmas. The dynamic characteristics are considered using an effective potential applicable at elevated pressure, but this is not a limitation. A three-species model capable of describing the collective processes is suggested, and a first order phase tran...

The dynamics of the ion structure in warm dense matter is determined by molecular dynamics simulations using an effective ion-ion potential. This potential is obtained from ab initio simulations and has a strong short-range repulsion added to a screened Coulomb potential. Models based on static or dynamic local field corrections are found to be ins...

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...

Los plasmas granulares son gases total o parcialmente ionizados que, además de iones electrones y átomos neutros, contienen partículas sólidas con carga eléctrica. Dichas partículas cargadas, de tama- ño mesoscópico, dan lugar a nuevos fenómenos colectivos con una dinámica característica. Este tipo de plasmas aparecen en sistemas físicos tan divers...

With the use of the method of moments applicable for any values of the parameter of the nonideality of a dusty plasma and
the hydrodynamic approach applicable only for small nonideality parameters, the theory of waves and oscillations of a complex
plasma has been generalized to the case of a two-exponential interaction potential. It has been shown...

The $e-e$, $e-i$, $i-i$ and charge-charge static structure factors are
calculated for alkali and Be$^{2+}$ plasmas using the method described by
Gregori et al. in \cite{bibGreg2006}. The dynamic structure factors for alkali
plasmas are calculated using the method of moments \cite{bibAdam83},
\cite{bibAdam93}. In both methods the screened Hellmann-G...

We review our approach to the modelling of optical properties of model moderately coupled plasmas. On the basis of the classical theory of moments the external and internal dynamic conductivities and the reflectivity coefficient of a model hydrogen moderately coupled plasma are determined using all known exact relations and sum rules. The sum rules...

The dynamic characteristics of strongly coupled one-component plasmas are studied within the moment approach. Our results on the dynamic structure factor and the dynamic local-field correction satisfy the sum rules and other exact relations automatically. A quantitative agreement is obtained with numerous simulation data on the plasma dynamic prope...

Dynamic characteristics of strongly coupled one-component plasmas are studied within the moment approach with local constraints, similar to that of Schur. The dynamic structure factor is modeled by the.rst three terms of its asymptotic decomposition at high frequencies and its values at a few interpolation points on the real axis. This makes the dy...

By definition, a Nevanlinna class function \(\varphi \in \Re\) is holomorphic and has a nonnegative imaginary part in the half-plane Im z > 0. In this chapter we also consider Nevanlinna functions which belong to the subclass \(\Re_0 \subset \Re\) such that if \(\varphi(z) \in \Re_0, \lim\nolimits_{z\to \infty} (\varphi(z)/z) = 0\), Im z > 0. Then,...

The method of moments is used to calculate the dynamic conductivity of strongly coupled fully ionized hydrogen plasmas. The electron density ne and temperature T vary in the domains 1021 < ne < 1024 cm−3, 104 K < T < 106 K. The results are compared to some theoretical data.

It has been recently shown that the Bethe-Larkin formula for the energy losses of fast heavy-ion projectiles in dense hydrogen plasmas is corrected by the electron-ion correlations [Phys. Rev. Lett. \textbf{101}, 075002 (2008)]. We report numerical estimates of this correction based on the values of $g_{ei}(0)$ obtained by numerical simulations in...

The Bethe-Larkin formula for the fast-projectile stopping power is extended to multicomponent plasmas. The results are to contribute to the correct interpretation of the experimental data, which could permit us to test existing and future models of thermodynamic, static, and dynamic characteristics of strongly coupled Coulomb systems.

The in-plane polarizational stopping power of heavy-ion diclusters in a two-dimensional strongly coupled electron liquid is studied. Analytical expressions for the stopping power of both fast and slow projectiles are derived. To go beyond the random-phase approximation we make use of the inverse dielectric function obtained by means of the method o...

We study the high-velocity-projectile limit of the polarizational
contribution to the in-plane stopping power in a strongly coupled
two-dimensional electron liquid. The dielectric formalism based on
the method of moments is employed. The frequency moments of the loss
function are calculated using the model Hamiltonian including the
two-dimensional...

Classical MD data on the charge-charge dynamic structure factor of two-component plasmas (TCP) modeled in Phys. Rev. A 23, 2041 (1981) are analyzed using the sum rules and other exact relations. The convergent power moments of the imaginary part of the model system dielectric function are expressed in terms of its partial static structure factors,...

Parameters of the two effective pseudopotentials in liquid alkali metals are determined. The approach is based on the solution of the Schrödinger equation with suitable pseudopotentials and the adjustment of the energy eigenvalues depending on the pseudopotential parameters to the corresponding atomic spectral data.

Dynamic properties of plasmas taking into account the electromagnetic field in the medium are considered. An effect of compensation of Coulomb correlations and its connection with the Langmuir mode is discussed.

The problem of calculation of the reflectivity of non-ideal shock-compressed plasmas is revisited. The dielectric formalism based on the method of moments incorporating exact asymptotic forms and sum rules is applied to the new experimental data. The approach is based on the Ansatz of reflection of laser radiation from a thin shock-front and posses...

In this work the previously developed method of calculation of HF electro-conductivity of non-ideal plasma is applied to the area of higher electron densities, up to 1024 cm-3 and in the temperature range 30 000 K ≤ T ≤ 200 000 K. The computations are carried out in the frequency range (0, 1·ωp), ωp being the plasma frequency. A good agreement with...

On the basis of numerically calculated values for the dense plasma dynamic conductivity in an external HF electric field, we determine the electrical permeability and the coefficients of refractivity and reflectivity of dense non-ideal plasmas. We consider electronic number density and temperature in the ranges of 10^{21} < N_{e} 10^{23} < cm^{−3}...

In this work, the previously developed method for calculation of HF electroconductivity of non-ideal plasma is applied to the area of high electron densities: 10(21) <= N-e <= 10(23) cm(-3) and in the temperature range 20000 K <= T <= 1000 000 K. This is enabled by the improvement of the numerical procedure. The real and imaginary parts of the HF c...

The description of all solutions of the truncated Stieltjes matrix moment problem consisting in finding all s × s matrix measures dσ (t) on [0,∞) with given first 2n+1 power s×s matrix moments (Cj)
j=0n
is obtained in a general case, when the block Hankel matrix Γn ≔ (Cj+k)
j,k=0n
may be non-invertible. Special attention is paid to the description...

The classical method of moments is applied to the analysis of the external and internal dynamic conductivities of dense plasmas. The Nevanlinna formula with only one nonzero f-sum rule taken into account reproduces the Drude-Lorentz model expression for the internal conductivity. The inclusion of the second non-zero sum rule produces a new model wh...

Asymptotic forms of the Hilbert-Scmidt and Hilbert norms of positive definite Toeplitz matrices $Q_{N}=(b(j-k))_{j,k=0}^{N-1}$ as $N\to \infty $ are determined. Here $b(j)$ are consequent trigonometric moments of a generating non-negative mesure $d\sigma (\theta)$ on $[ -\pi ,\pi ] $. It is proven that $\sigma (\theta)$ is continuous if and only if...

A dynamic longitudinal internal conductivity model, derived from the classical method of moments, is applied to the analysis of recent simulation data and reflectivity measurements of shock-compressed dense xenon plasmas. This model satisfies both the non-zero f–sum rule and the second non-zero sum rule, and reproduces the non-monotonicity of the c...

A method for beam shaping based on fitting the power moments of the final beam intensity distribution and independent of the optical system particularities is suggested. It is shown how one can analytically calculate any moment of the final phase space distribution using the moments of the initial distribution and the optical system transfer map. N...

The dynamic electric conductivity, dielectric permeability and refraction and reflection coefficients of a completely ionized gaseous plasma in a high frequency (HF) external electric field are calculated. These results are obtained within the self-consistent field approach developed earlier for the static conductivity determination. The plasma ele...

The truncated Hamburger and Stieltjes moment problems [1] were solved elsewhere (see [3] and references therein) using the methods of the extension theory of Hermitian operators and, in particular, the results on extensions of nonnegative operators and matrices. Moreover, applying methods of the extension theory we found a purely algebraic algorith...

Self-consistent and universal description of friction and diffusion for Brownian particles in such various systems as dusty plasma and active particles (e.g., cells in biological systems) is presented. Generalized friction function is determined to describe the friction force itself as well as a drag force in the case of non-zero driven ion velocit...

A complex response function describing a reaction of a multi-particle system to a weak alternating external field is the boundary value of a Nevanlinna class function (i.e. a holomorphic function with non-negative imaginary part in the upper half-plane). Attempts of direct calculations of response functions based on standard approximations of the k...

Earlier theoretical and computer studies on the dynamics of strongly coupled charged particle bilayers have revealed the existence of an energy gap (ω(k = 0) ≠ 0, optical behaviour) for the out-of-phase plasmon. This is in contrast to the correlationless RPA prediction of acoustic (ω ~ k) behaviour. We have studied the question whether a classical...

The conditions of solvability and description of all solu-tions of the truncated Stieltjes moment problem are obtained using as the starting point earlier results on the Hamburger truncated moment problem. An algebraic algorithm for the explicit solution of both prob-lems is proposed.

The interpolation problem of constructing a function holomorphic on the upper half-plane with values having nonnegative imaginary part and with continuous extension to the real axis by the first 2n+1 terms of its asymptotic decomposition at infinity and its values at some m points of the real axis is solved using algorithms which are reminiscent of...

A quantitative evaluation of linear energy losses of heavy particles in dense plasmas is achieved on the basis of the rational approximation for the plasma dielectric function generated by the method of moments. A comparison with the simulation data is carried out. The asymptotic behavior of the plasma stopping power is studied in detail.

A self-consistent field theory of transport properties of strongly coupled, fully ionized, multicomponent plasmas is successfully applied to real and model plasmas. In addition, a soft interpolation is found between the Monte-Carlo OCP equation of state and the low-density exact expansion by Abe.

In this paper the dispersion laws for electromagnetic waves in cold magnetized plasmas are analyzed. The basis of our analysis was the expression for the dielectric tensor obtained from the classical theory of moments. The dielectric tensor is constructed without using the perturbation theory. Thus both the case of weak and strong Coulomb coupling...

The interpolation problem of reconstruction of a holomorphic in the upper half-plane function with non-negative imaginary part and continuous boundary value on the real axis by the first 2n + 1 terms of its asymptotic decomposition at infinity and its values at some m points of the real axis is solved using algorithms, which are reminiscent of thos...

The canonical solutions of the truncated Hamburger mo-ment problem (both in the classical and degenerate cases) are found. The Nevanlinna theorem which provides the noncanonical solutions of the truncated Hamburger problem is also rederived in the framework of the operator approach.

The stopping power of coupled electronic plasmas is investigated. Within the dielectric formalism and employing the method of frequency moments for the dielectric function we obtain a general formula describing the linear stopping power of a coupled plasma. Analytical results for the low- and high-projectile-velocity asymptotic forms are obtained....