Local Field Correction Research Articles

Structure-induced order – disorder transformation in Cd – Na liquid alloys

Abstract The origins of the S-shaped entropy of mixing and order – disorder transformation in Cd –Na liquid alloys have been investigated within a first-principle approach of a pseudo-potential perturbation scheme with the Gibbs–Bogoliubov variation technique.We find that the deepening of the structure part of the entropy around the stoichiometric composition (c Na ≈ 0.33) is responsible for the S-shaped entropy and suggests the existence of short-range order in the liquid state. The role of the local-field correction function, G(q), of conduction electrons on the entropy of mixing is examined. The impact of G(q) on partial structure factors is more visible towards low q (q → 0) than at higher q.

Integral equation theory based dielectric scheme for strongly coupled electron liquids.

In a recent paper, Lucco Castello et al. (arXiv:2107.03537) provided an accurate parameterization of classical one-component plasma bridge functions that was embedded in a novel dielectric scheme for strongly coupled electron liquids. Here, this approach is rigorously formulated, its set of equations is formally derived, and its numerical algorithm is scrutinized. A systematic comparison with available and new path integral Monte Carlo simulations reveals a rather unprecedented agreement especially in terms of the interaction energy and the long wavelength limit of the static local field correction.

Density response of the warm dense electron gas beyond linear response theory: Excitation of harmonics

In a recent Letter, Dornheim et al. [PRL 125, 085001 (2020)] have investigated the nonlinear density response of the uniform electron gas in the warm dense matter regime. More specifically, they have studied the cubic response function at the first harmonic, which cannot be neglected in many situations of experimental relevance. In this work, we go one step further and study the full spectrum of excitations at the higher harmonics of the original perturbation based on extensive new ab initio path integral Monte Carlo (PIMC) simulations. We find that the dominant contribution to the density response beyond linear response theory is given by the quadratic response function at the second harmonic in the moderately nonlinear regime. Furthermore, we show that the nonlinear density response is highly sensitive to exchange-correlation effects, which makes it a potentially valuable new tool of diagnostics. To this end, we present a new theoretical description of the nonlinear electronic density response based on the recent effective static approximation to the local field correction [PRL 125, 235001 (2020)], which accurately reproduces our PIMC data with negligible computational cost.

Ion core effect on scattering processes in dense plasmas

A pseudopotential approach was used to study the effect of an ionic core on the electron–ion scattering in dense plasmas. Screening of the ion charge is taken into account using the density response function in the long wavelength limit. Additionally, the effect of electronic non-ideality is included using the compressibilty sum-rule connecting the local field correction and the exchange-correlation part of the electronic free energy density. Using a screened pseudopotential, we have computed electron–ion scattering phase shifts, the total elastic scattering cross section, and the transport cross section. It is found that the ionic core leads to the strong decrease in the scattering cross sections. Additionally, it is shown that the transport cross section has a non-monotonic dependence on the variation of the ionic core field parameters.

Local field correction to ionization potential depression of ions in warm or hot dense matter.

An analytical self-consistent approach was recently established to predict the ionization potential depression (IPD) in multicomponent dense plasmas, which is achieved by considering the self-energy of ions and electrons within the quantum statistical theory. In order to explicitly account for the exchange-correlation effect of electrons, we incorporate the effective static approximation of local field correction (LFC) within our IPD framework through the connection of dynamical structure factor. The effective static approximation poses an accurate description for the asymptotic large wave number behavior with the recently developed machine learning representation of static LFC induced from the path-integral Monte Carlo data. Our calculation shows that the introduction of static LFC through dynamical structure factor brings a nontrivial influence on IPD at warm/hot dense matter conditions. The correlation effect within static LFC could provide up to 20% correction to free-electron contribution of IPD in the strong coupling and degeneracy regime. Furthermore, a new screening factor is obtained from the density distribution of free electrons calculated within the average-atom model, with which excellent agreements are observed with other methods and experiments at warm/hot dense matter conditions.

The local-field correction factor beyond the Onsager–Böttcher approach: Mixing of states from the interaction with atoms in the surrounding medium

The radiative transition of an emitter dipole is a fundamental process in many natural phenomena and can be modified by a dielectric environment. The Onsager–Böttcher (OB) approach predicts the experimental results in the frame of the local-field correction; however, there remains controversy when the macroscopic approximation is used. In this work, the main mechanism to explain the local-field correction arises dynamic coupling (DC). Although the OB and DC models consider the effect of the polarisation of the neighbouring atoms (NN) from the emitter and from the electric field of the light, respectively, we show that these effects arise naturally when the mixing of states from the interaction with the atoms in the surrounding medium is considered. Using perturbation theory, we show that the local field depends on the polarisability of the NN, and in contrast to the OB model, the concept of the polarisability of an emitter in transition is not necessary. Our expression is reduced to the OB model when the NN have spherical symmetry and do not absorb light.

Dust-Acoustic Wave Dispersion in Thermal Dusty Plasmas at Weak and Moderate Couplings

The dispersion of dust-acoustic waves (DAWs) in weakly and moderately coupled thermal dusty plasmas is studied in the framework of the linear density-response formalism with the static local-field correction for interdust interactions. The plasma medium composition and the charge of dust particles are simultaneously determined within a recently developed chemical model (Physical Review E, vol. 101, 063203, 2020) based on minimizing the Helmholtz free energy of the system under investigation. Stemming from the generalized Poisson-Boltzmann equation, the renormalization procedure is consistently applied to derive an interdust screened potential that takes into account the finiteness of dust grains. Within the framework of the Ornstein-Zernike relationship in the hypernetted chain approximation, the static structure factor of the dust component is evaluated to manifest the appearance of local extrema on its wavenumber dependence, thereby indicating the short-range order formation in the arrangement of dust particles with respect to one another. It is shown that the DAW dispersion law is completely governed by the static structure factor and, therefore, exhibits a nonmonotonic dependence on the wavenumber as well. In the long-wavelength limit, the acoustic-like behavior of the DAW dispersion is strictly confirmed and the corresponding phase speed, reduced in units of the dust thermal velocity, is ultimately expressed via the static structure factor at zero wavenumber.

Analytical representation of the local field correction of the uniform electron gas within the effective static approximation

The description of electronic exchange--correlation effects is of paramount importance for many applications in physics, chemistry, and beyond. In a recent Letter, Dornheim \textit{et al.} [\textit{Phys. Rev. Lett.}~\textbf{125}, 235001 (2020)] have presented the \emph{effective static approximation} (ESA) to the local field correction (LFC), which allows for the highly accurate estimation of electronic properties such as the interaction energy and the static structure factor. In the present work, we give an analytical parametrization of the LFC within ESA that is valid for any wave number, and available for the entire range of densities ($0.7\leq r_s \leq20$) and temperatures ($0\leq \theta\leq 4$) that are relevant for applications both in the ground state and in the warm dense matter regime. A short implementation in Python is provided, which can easily be incorporated into existing codes. In addition, we present an extensive analysis of the performance of ESA regarding the estimation of various quantities like the dynamic structure factor, static dielectric function, the electronically screened ion-potential, and also stopping power in electronic medium. In summary, we find that the ESA gives an excellent description of all these quantities in the warm dense matter regime, and only becomes inaccurate when the electrons start to form a strongly correlated electron liquid ($r_s\sim20$). Moreover, we note that the exact incorporation of exact asymptotic limits often leads to a superior accuracy compared to the neural-net representation of the static LFC [\textit{J.~Chem.~Phys.}~\textbf{151}, 194104 (2019)].

Drag resistivity in bilayer-graphene/GaAs coupled layer system with the effect of local field corrections

Drag resistivity mediated by Coulomb interaction is a transport phenomenon in a specially separated bilayer systems. The drag resistivity is numerically analysed for both the n- and p-type charge carriers between the bilayer-graphene and a GaAs layer, with an insulating barrier by using random phase approximation (RPA). The RPA method does not include exchange and correlation effects, which are included by assuming the local field correction (LFC) in effective interactions. Because of the LFC effects, the drag resistivity is found enhanced compared to the measured results of RPA. The present bilayer system shows a comparison between effect of electron–electron (e–e) repulsive and electron–hole (e–h) attractive interactions in Boltzmann regime for low temperature limit. Different masses of electrons and holes in GaAs layer are analysed, and drag resistivity is increased on increasing the effective mass of the charge carriers. The dependency of drag resistivity on temperature, concentration, interlayer separation, width of the drag layer and dielectric constant of barrier shows a consistent behaviour.

Study of coulomb drag with the effect of local field correction and dielectric medium

We present a numerical calculation for the drag resistivity of charge carriers interaction in coupled layer system separated by a barrier. Analytical expressions of non-linear susceptibility function and effective interlayer Coulomb interaction have been shown for non homogeneous dielectric environment at low temperature and low frequency regime. The system is studied within the model of random phase approximation (RPA) and taking into account the static local field correction (LFC). We employ Hubbard approximations (HA) and self consistent STLS approximations based LFC for obtaining the results, where LFC includes the exchange and correlation effects. Exchange and correlation effects enhanced the drag resistivity and the net screening. Another important quantity is the local form factors (LFF), which is the function of the bare inter- and intra-layer potential of the dielectric media. LFF for a multi-layer system is derived from the Poisson equation solution.

Study of drag resistivity in dielectric medium with the correlations effect

We study the drag resistivity numerically for charge carriers in a specially separated electron-electron (e-e) bilayer system for both the symmetric and asymmetric case in weak interaction and Boltzmann regime. Interaction in Coulomb drag effect is based on Coulomb interaction in a specially separated bilayer systems. Random phase approximation (RPA) method is used to find the drag resistivity. Simply RPA method is a reliable method for high-density regime where exchange and correlation effects do not impact too much. On lowering the density, the exchange and correlation effects are significant which are included by suggesting the local field correction (LFC) in effective interlayer interactions. The drag resistivity is noticed improvement on employing the LFC. Impact of exchange and correlation based LFC increase on increasing the temperature and decreasing the concentration. Predictable behaviour is shown by the dependency of drag resistivity on temperature, density, interlayer spacing, and dielectric constant.

First-principles modeling of plasmons in aluminum under ambient and extreme conditions

The theoretical understanding of plasmon behavior is crucial for an accurate interpretation of inelastic scattering diagnostics in many experiments. We highlight the utility of linear response time-dependent density functional theory (LR-TDDFT) as a first-principles framework for consistently modeling plasmon properties. We provide a comprehensive analysis of plasmons in aluminum from ambient to warm dense matter conditions and assess typical properties such as the dynamical structure factor, the plasmon dispersion, and the plasmon lifetime. We compare our results with scattering measurements and with other TDDFT results as well as models such as the random phase approximation, the Mermin approach, and the dielectric function obtained using static local field corrections of the uniform electron gas parametrized from path-integral Monte Carlo simulations. We conclude that results for the plasmon dispersion and lifetime are inconsistent between experiment and theories and that the common practice of extracting and studying plasmon dispersion relations is an insufficient procedure to capture the complicated physics contained in the dynamic structure factor in its full breadth.

Description of longitudinal modes in moderately coupled Yukawa systems with the static local field correction

In moderately coupled Yukawa fluids, longitudinal mode dispersion is determined by the competition between kinetic and potential effects. In a recent paper [S. Khrapak and L. Couëdel, Phys. Rev. E 102, 033207 (2020)], a semi-phenomenological dispersion relation was constructed by the ad hoc addition of the Bohm–Gross kinetic term to the generalized instantaneous excess bulk modulus, which showed very good agreement with simulations. In this paper, a nearly identical dispersion relation is derived in a rigorous manner based on a dielectric formulation with static local field corrections. At moderate coupling, this formalism is revealed to be more accurate than other successful theoretical approaches.

Screening of a test charge in a free‐electron gas at warm dense matter and dense non‐ideal plasma conditions

AbstractThe screening of a test charge by partially degenerate non‐ideal free electrons at conditions related to warm dense matter and dense plasmas is investigated using linear response theory and the local field correction based on ab initio Quantum Monte‐Carlo simulations data. The analysis of the obtained results is performed by comparing to the random phase approximation and the Singwi–Tosi–Land–Sjölander approximation. The applicability of the long‐wavelength approximation for the description of screening is investigated. The impact of electronic exchange‐correlations effects on structural properties and the applicability of the screened potential from linear response theory for the simulation of the dynamics of ions are discussed.

Investigation of some basic thermodynamic properties of Na-K alloy

Investigation of thermodynamic of liquid binary alloys using pseudopotential theory is reported. The potential suggested by Fiolhais et al. with its individual parameters is used for the entire calculation. A transferability of the potential from the solid to liquid medium is achieved for the presently reported binary alloy. The internal energy components, Helmholtz free energy, entropy, and total energy at various proportions of the participating alkali metals are included in the study. The comparison with the other data has been shown in the present article. Exchange and correlation effect is also tested with the help of various local field correction functions.
 BIBECHANA 18 (2) (2021) 1-8

Local Stress Field Correction Method Based on a Genetic Algorithm and a BP Neural Network for In Situ Stress Field Inversion

The in situ stress field is the fundamental factor causing deformation and damage in geotechnical engineering, so it is the main basis for underground engineering design and excavation. However, it is difficult to accurately obtain the in situ stress through most existing inversion methods in areas with complex geological conditions. For the problem of a relatively discrete and nonlinear relationship of measured stress in the Yebatan Hydropower Station area, a new in situ stress inversion method called the local stress field correction (LSFC) method combining a genetic algorithm (GA), backpropagation (BP) neural network, and submodel method is proposed. The inverted in situ stress results produced by this method show that the distribution of in situ stress is greatly influenced by tectonic movements in the Yebatan area, there is no obvious linear relationship with depth, and the stress release phenomenon occurs at the faults. By comparison with the multiple regression method, it is found that the method still has high inversion accuracy under complex geological conditions, and the average relative error of LSFC inversion results is 17.05%, which is much lower than the value of 43.58% via the multiple regression method. Therefore, the LSFC method can be used for the inversion of in situ stress in complex geological regions and provide a reference for engineering design and construction.

A unified study of electrical transport properties of some liquid metals by pseudopotential method

A well-recognized local pseudopotential is utilized to study the electrical transport properties such as electrical resistivity (ρ), thermal conductivity (σ) and thermoelectric power (TEP) of some liquid metals. The model potential theory in combination with Ziman, mean free path and Kubo models are implemented in the aforesaid study. The Taylor’s local field correction function is taken for studying the exchange and correlation effect with one component plasma (OCP) structure factor method of liquid metals. The computed data is found highly appreciated order with available either theoretical or experimental outcomes wherever exits.

A Variational Technique for Thermodynamics of Liquid K(1-x)Rbx Alloys

Liquid K_(1-x) Rb_x binary alloys with various thermodynamical proportions of participating elements are investigated. The properties of thermodynamic interest are included in the study. The internal energy (Fint), Helmholtz free enrgy (FH) and the entropy (S) have been calculated in a concentration range from X=0.0 to X=1.0 increasing in a step of 0.1 in the present work. Apart from the internal energy (Fint), various contributions to this energy are also calculated and separately depicted in the present article. A variational approach has been adopted for the present calculation. A single potential with a set of two parameters is used for the calculation of all properties of the alloys. Static Hartree local field function (H) is used to consider screening effect. Various local field correction functions are used to take into account the exchange and correlation effect. Comparison with experimental data at some concentration shows the good agreement with the presently obtained data. With the help of current results, the applied model potential found very suitable with individual parameters for thermodynamical study. As the present results provide the data even where minimum availability of the experimental findings, it can serve as a data base for the future calculation which deals with thermodynamics of the liquid alloys. Present results allow one to get proportion based tuned properties of the K_(1-x) Rb_x for different requirements.

A study of collective modes of Zr41Ti14Cu12.5Be22.5Fe10 bulk metallic glass and estimation of thermodynamic and elastic properties using pseudopotential theory

The collective modes of Zr41Ti14Cu12.5Be22.5Fe10 bulk metallic glass (BMG) have been theoretically studied using pseudopotential formalism. Shaw’s optimized model potential is used to describe effective interactions. Five different forms of the local field correction functions, viz. Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) have been exploited with modified Bhatia-Singh (BS) computational approach to examine the relative influence of exchange and correlation effects and to reproduce longitudinal and transverse modes of phonon eigenfrequencies using phonon dispersion curves (PDCs). Important thermodynamic and elastic properties are calculated by long-wavelength limits of phonon modes. The comparisons of such properties with earlier reported data are shown good agreement.

Effective Static Approximation: A Fast and Reliable Tool for Warm-Dense Matter Theory.

We present an effective static approximation (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor S(q,ω), the static structure factor S(q), and the interaction energy v. The ESA combines the recent neural-net representation by T. Dornheim et al., [J. Chem. Phys. 151, 194104 (2019)JCPSA60021-960610.1063/1.5123013] of the temperature-dependent LFC in the exact static limit with a consistent large wave-number limit obtained from quantum MonteCarlo data of the on-top pair distribution function g(0). It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by reevaluating the results of the recent x-ray Thomson scattering experiment on aluminum by Sperling etal. [Phys. Rev. Lett. 115, 115001 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.115001]. We find that an accurate incorporation of electronic correlations in terms of the ESA leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like the Mermin approach or linear-response time-dependent density functional theory. Furthermore, the ESA scheme is particularly relevant for the development of advanced exchange-correlation functionals in density functional theory.