The method of effective potentials in the quantum-statistical theory of plasmas

Development of a new quantum trajectory molecular dynamics framework

An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Exchange-correlation bound states of the triplet soft-sphere fermions by path-integral Monte Carlo simulations

Path-integral Monte Carlo simulations in the Wigner approach to quantum mechanics has been applied to calculate momentum and spin-resolved radial distribution functions of the strongly correlated soft-sphere quantum fermions. The obtained spin-resolved radial distribution functions demonstrate arising triplet clusters of fermions, that is the consequence of the interference of exchange and interparticle interactions. The semiclassical analysis in the framework of the Bohr-Sommerfeld quantization condition, applied to the potential of the mean force corresponding to the same-spin radial distribution functions, allows to detect exchange-correlation bound states in triplet clusters and to estimate corresponding averaged energy levels. The obtained momentum distribution functions demonstrate the narrow sharp separated peaks corresponding to bound states and disturbing the Maxwellian distribution.

Bound States of the Exchange—Correlation Excitons in the Uniform Electron Gas by the Monte Carlo Simulations

The modified path integral representation of Wigner functions and the new Monte Carlo approach has been suggested to account for the impact of the interparticle interaction on the Pauli exclusion principle of fermions. This approach also allows to calculate the momentum distribution functions and to reduce the “sign problem” that is inaccessible to the standard path integral Monte Carlo methods. The obtained pair electron–electron distribution functions for the “uniform electron gas” demonstrate the short-range quantum ordering of electrons associated with exchange–correlation excitons. The exchange–correlation exciton is caused by the interaction of electrons with positively charged exchange holes and the excluded volume effect. The developed approach allows one to study the density–temperature range of the exciton arising, existence, and decay. Using the potential of the mean force and semiclassical Bohr–Sommerfeld quantization condition, we have demonstrated the existence of bound states disturbing the Maxwellian distribution and estimated their average energy levels. The exchange–correlation excitons have not been observed earlier in the standard path integral Monte Carlo simulations.

Momentum distribution function and short-range correlations of the warm dense electron gas: Ab initio quantum Monte Carlo results

In a classical plasma the momentum distribution, n(k), decays exponentially, for large k, and the same is observed for an ideal Fermi gas. However, when quantum and correlation effects are relevant simultaneously, an algebraic decay, n_{∞}(k)∼k^{-8} has been predicted. This is of relevance for cross sections and threshold processes in dense plasmas that depend on the number of energetic particles. Here we present extensive ab initio results for the momentum distribution of the nonideal uniform electron gas at warm dense matter conditions. Our results are based on first principle fermionic path integral Monte Carlo (CPIMC) simulations and clearly confirm the k^{-8} asymptotic. This asymptotic behavior is directly linked to short-range correlations which are analyzed via the on-top pair distribution function (on-top PDF), i.e., the PDF of electrons with opposite spin. We present extensive results for the density and temperature dependence of the on-top PDF and for the momentum distribution in the entire momentum range.

Fermionic path-integral Monte Carlo results for the uniform electron gas at finite temperature

The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the experimental progress in the field of warm dense matter. To explain the experimental data, accurate theoretical models for high-density plasmas are needed that depend crucially on the quality of the thermodynamic properties of the quantum degenerate nonideal electrons and of the treatment of their interaction with the positive background. Recent fixed-node path-integral Monte Carlo (RPIMC) data are believed to be the most accurate for the UEG at finite temperature, but they become questionable at high degeneracy when the Brueckner parameter rs=a/aB--the ratio of the mean interparticle distance to the Bohr radius--approaches 1. The validity range of these simulations and their predictive capabilities for the UEG are presently unknown. This is due to the unknown quality of the used fixed nodes and of the finite-size scaling from N=33 simulated particles (per spin projection) to the macroscopic limit. To analyze these questions, we present alternative direct fermionic path integral Monte Carlo (DPIMC) simulations that are independent from RPIMC. Our simulations take into account quantum effects not only in the electron system but also in their interaction with the uniform positive background. Also, we use substantially larger particle numbers (up to three times more) and perform an extrapolation to the macroscopic limit. We observe very good agreement with RPIMC, for the polarized electron gas, up to moderate densities around rs=4, and larger deviations for the unpolarized case, for low temperatures. For higher densities (high electron degeneracy), rs≲1.5, both RPIMC and DPIMC are problematic due to the increased fermion sign problem.

Wave packet spreading and localization in electron-nuclear scattering

The wave packet molecular dynamics (WPMD) method provides a variational approximation to the solution of the time-dependent Schrödinger equation. Its application in the field of high-temperature dense plasmas has yielded diverging electron width (spreading), which results in diminishing electron-nuclear interactions. Electron spreading has previously been ascribed to a shortcoming of the WPMD method and has been counteracted by various heuristic additions to the models used. We employ more accurate methods to determine if spreading continues to be predicted by them and how WPMD can be improved. A scattering process involving a single dynamic electron interacting with a periodic array of statically screened protons is used as a model problem for comparison. We compare the numerically exact split operator Fourier transform method, the Wigner trajectory method, and the time-dependent variational principle (TDVP). Within the framework of the TDVP, we use the standard variational form of WPMD, the single Gaussian wave packet (WP), as well as a sum of Gaussian WPs, as in the split WP method. Wave packet spreading is predicted by all methods, so it is not the source of the unphysical diminishing of electron-nuclear interactions in WPMD at high temperatures. Instead, the Gaussian WP's inability to correctly reproduce breakup of the electron's probability density into localized density near the protons is responsible for the deviation from more accurate predictions. Extensions of WPMD must include a mechanism for breakup to occur in order to yield dynamics that lead to accurate electron densities.

Electron-ion and ion-ion potentials for modeling warm dense matter: Applications to laser-heated or shock-compressed Al and Si

The pair interactions Uij(r) determine the thermodynamics and linear transport properties of matter via the pair-distribution functions (PDFs), i.e., gij(r). Great simplicity is achieved if Uij(r) could be directly used to predict material properties via classical simulations, avoiding many-body wave functions. Warm dense matter (WDM) is encountered in quasiequilibria where the electron temperature Te differs from the ion temperature Ti, as in laser-heated or in shock-compressed matter. The electron PDFs gee(r) as perturbed by the ions are used to evaluate fully nonlocal exchange-correlation corrections to the free energy, using hydrogen as an example. Electron-ion potentials for ions with a bound core are discussed with Al and Si as examples, for WDM with Te≠Ti, and valid for times shorter than the electron-ion relaxation time. In some cases the potentials develop attractive regions and then become repulsive and "Yukawa-like" for higher Te. These results clarify the origin of initial phonon hardening and rapid release. Pair potentials for shock-heated WDM show that phonon hardening would not occur in most such systems. Defining meaningful quasiequilibrium static transport coefficients consistent with the dynamic values is addressed. There seems to be no meaningful "static conductivity" obtainable by extrapolating experimental or theoretical σ(ω,Ti,Te) to ω→0, unless Ti→Te as well. Illustrative calculations of quasistatic resistivities R(Ti,Te) of laser-heated as well as shock-heated aluminum and silicon are presented using our pseudopotentials, pair potentials, and classical integral equations. The quasistatic resistivities display clear differences in their temperature evolutions, but are not the strict ω→0 limits of the dynamic values.

Wave packet simulation of dense hydrogen

Dense hydrogen is studied in the framework of wave packet molecular dynamics. In this semiquantal many-body simulation method the electrons are represented by wave packets which are suitably parametrized. The equilibrium properties and time evolution of the system are obtained with the help of a variational principle. At room temperature the results for the isotherms are in good agreement with anvil experiments. At higher densities beyond the range of the experimental data a transition from a molecular to a metallic state is predicted. The wave packets become delocalized and the electrical conductivity increases sharply. The phase diagram is calculated in a wide range of the pressure-density-temperature space. The observed transition from the molecular to metallic state is accompanied by an increase in density in agreement with recent reverberating shock wave experiments.

Collective and static properties of model two-component plasmas

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, which are computed by the method of hypernetted chains using the Deutsch effective potential. High-frequency asymptotic behavior of the dielectric function is specified to include the effects of inverse bremsstrahlung. The agreement with the MD data is improved, and important statistical characteristics of the model TCP, such as the probability to find both electron and ion at one point, are determined.

Correlation effects in partially ionized mass asymmetric electron-hole plasmas

The effects of strong Coulomb correlations in dense three-dimensional electron-hole plasmas are studied by means of unbiased direct path integral Monte Carlo simulations. The formation and dissociation of bound states, such as excitons and biexcitons, is analyzed and the density-temperature region of their appearance is identified. At high density, the Mott transition to the fully ionized metallic state (electron-hole liquid) is detected. Particular attention is paid to the influence of the hole to electron mass ratio M on the properties of the plasma. Above a critical value of about M=80 formation of a hole Coulomb crystal was recently verified [Bonitz, Phys. Rev. Lett. 95, 235006 (2005)] which is supported by additional results. Results are related to the excitonic phase diagram of intermediate valent Tm[Se,Te], where large values of M have been observed experimentally.