Fully variational average atom model with ion-ion correlations

Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods

Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory but offer higher accuracy. Accordingly, quantum computers have been predominantly regarded as competitors to only the most accurate and costly classical methods for treating electron correlation. However, here we tighten bounds showing that certain first-quantized quantum algorithms enable exact time evolution of electronic systems with exponentially less space and polynomially fewer operations in basis set size than conventional real-time time-dependent Hartree-Fock and density functional theory. Although the need to sample observables in the quantum algorithm reduces the speedup, we show that one can estimate all elements of the k-particle reduced density matrix with a number of samples scaling only polylogarithmically in basis set size. We also introduce a more efficient quantum algorithm for first-quantized mean-field state preparation that is likely cheaper than the cost of time evolution. We conclude that quantum speedup is most pronounced for finite-temperature simulations and suggest several practically important electron dynamics problems with potential quantum advantage.

Variational atomic model of plasma accounting for ion radial correlations and electronic structure of ions

We propose a model of ion-electron plasma (or nucleus-electron plasma) that accounts for the electronic structure around nuclei (i.e., ion structure) as well as for ion-ion correlations. The model equations are obtained through the minimization of an approximate free-energy functional, and it is shown that the model fulfills the virial theorem. The main hypotheses of this model are (1) nuclei are treated as classical indistinguishable particles, (2) electronic density is seen as a superposition of a uniform background and spherically symmetric distributions around each nucleus (system of ions in a plasma), (3) free energy is approached using a cluster expansion (nonoverlapping ions), and (4) resulting ion fluid is modeled through an approximate integral equation. In the present paper, the model is described only in its average-atom version.

Enhancement of electron-impact ionization induced by warm dense environments

Studies have shown significant discrepancies between the recent experiment [Berg et al., Phys. Rev. Lett. 120, 055002 (2018)PRLTAO10.1103/PhysRevLett.120.055002] and current theoretical calculations on the electron-impact ionization cross section of ions in warm dense magnesium. Here, we present a systematic study the effects of the ionic correlations and free-electron screening on the electron-impact ionization of ions in warm dense matter. The ionic correlation and the free-electron screening effects yield additional Hermitian terms to the calculation of the ionic central-force-field potential, which significantly change the electronic structure compared with that of the isolated ion. In calculating the electron-impact ionization, we describe the impact and ionized electrons using a damped-distorted wave function, which considers the momentum relaxation of free electrons due to collisions with other free electrons and ions. We reproduce the electron-impact ionization process for Mg^{7+} in the solid-density plasma and increase the ionization cross section by one order of magnitude compared with that of the isolated ion, which excellently agrees with the experimental result of Berg et al.

Kinetic model for electron-ion transport in warm dense matter

We present a model for electron-ion transport in warm dense matter that incorporates Coulomb coupling effects into the quantum Boltzmann equation of Uehling and Uhlenbeck through the use of a statistical potential of mean force. Although the model presented here can be derived rigorously in the classical limit [S. D. Baalrud and J. Daligault, Phys. Plasmas 26, 082106 (2019)PHPAEN1070-664X10.1063/1.5095655], its quantum generalization is complicated by the uncertainty principle. Here we apply an existing model for the potential of mean force based on the quantum Ornstein-Zernike equation coupled with an average-atom model [C. E. Starrett, High Energy Density Phys. 25, 8 (2017)1574-181810.1016/j.hedp.2017.09.003]. This potential contains correlations due to both Coulomb coupling and exchange, and the collision kernel of the kinetic theory enforces Pauli blocking while allowing for electron diffraction and large-angle collisions. We use the Uehling-Uhlenbeck equation to predict the momentum and temperature relaxation times and electrical conductivity of solid density aluminum plasma based on electron-ion collisions. We present results for density and temperature conditions that span the transition from classical weakly-coupled plasma to degenerate moderately-coupled plasma. Our findings agree well with recent quantum molecular dynamics simulations.

Consistent approach for electrical resistivity within Ziman's theory from solid state to hot dense plasma: Application to aluminum

The approach presented in this work allows a consistent calculation of electrical conductivity of dense matter from the solid state to the hot plasma using the same procedure, consisting in dropping elastic scattering contributions to solid's and liquid's structure factors in the framework of the Ziman theory. The solid's structure factor was computed using a multiphonon expansion. The elastic part is the zero-phonon term and corresponds to Bragg peaks, thermally damped by Debye-Waller attenuation factors. For the liquid, a similar elastic contribution to the structure factor results from a long-range order persisting during the characteristic electron-ion scattering time. All the quantities required for the calculation of the resistivities are obtained from our average-atom model, including the total hypernetted-chain structure factor used from the liquid state to the plasma. No interpolation between two limiting structure factors is required. We derive the correction to apply to the resistivity in order to account for the transient long-range order in the liquid and show that it improves considerably the agreement with quantum-molecular dynamics simulations and experimental aluminum's isochoric and isobaric conductivities. Our results suggest that the long-range order in liquid aluminum could be a slightly compressed fcc one. Two series of ultrafast experiments performed on aluminum were also considered, the first one by Milchberg et al. using short laser pulses and the second one by Sperling et al. involving x-ray heating and carried out on the Linac Coherent Light Source facility. Our attempts to explain the latter assuming an initial liquid state at an ion temperature much smaller than the electron one suggest that the actual initial state before main heating is neither perfectly solid nor a normal liquid.

Simpler free-energy functional of the Debye-Hückel model of fluids and the nonuniqueness of free-energy functionals in the theory of fluids

In previous publications [Piron and Blenski, Phys. Rev. E 94, 062128 (2016)2470-004510.1103/PhysRevE.94.062128; Blenski and Piron, High Energy Density Phys. 24, 28 (2017)1574-181810.1016/j.hedp.2017.05.005], the authors have proposed Debye-Hückel-approximate free-energy functionals of the pair distribution functions for one-component fluids and two-component plasmas. These functionals yield the corresponding Debye-Hückel integral equations when they are minimized with respect to the pair distribution functions, lead to correct thermodynamic relations, and fulfill the virial theorem. In the present paper, we update our results by providing simpler functionals that have the same properties. We relate these functionals to the approaches of Lado [Phys. Rev. A 8, 2548 (1973)0556-279110.1103/PhysRevA.8.2548] and of Olivares and McQuarrie [J. Chem. Phys. 65, 3604 (1976)JCPSA60021-960610.1063/1.433545]. We also discuss briefly the nonuniqueness issue that is raised by these results.

Dynamic electron-ion collisions and nuclear quantum effects in quantum simulation of warm dense matter

The structural, thermodynamic and transport properties of warm dense matter (WDM) are crucial to the fields of astrophysics and planet science, as well as inertial confinement fusion. WDM refers to the states of matter in a regime of temperature and density between cold condensed matter and hot ideal plasmas, where the density is from near-solid up to ten times solid density, and the temperature between 0.1 and 100 eV. In the WDM regime, matter exhibits moderately or strongly coupled, partially degenerate properties. Therefore, the methods used to deal with condensed matter and isolated atoms need to be properly validated for WDM. It is therefore a big challenge to understand WDM within a unified theoretical description with reliable accuracy. Here, we review the progress in the theoretical study of WDM with state-of-the-art simulations, i.e. quantum Langevin molecular dynamics and first principles path integral molecular dynamics. The related applications for WDM are also included.

Correlation and transport properties for mixtures at constant pressure and temperature

Transport properties of mixtures of elements in the dense plasma regime play an important role in natural astrophysical and experimental systems, e.g., inertial confinement fusion. We present a series of orbital-free molecular dynamics simulations on dense plasma mixtures with comparison to a global pseudo ion in jellium model. Hydrogen is mixed with elements of increasingly high atomic number (lithium, carbon, aluminum, copper, and silver) at a fixed temperature of 100 eV and constant pressure set by pure hydrogen at 2g/cm^{3}, namely, 370 Mbars. We compute ionic transport coefficients, such as self-diffusion, mutual diffusion, and viscosity for various concentrations. Small concentrations of the heavy atoms significantly change the density of the plasma and decrease the transport coefficients. The structure of the mixture evidences a strong Coulomb coupling between heavy ions and the appearance of a broad correlation peak at short distances between hydrogen atoms. The concept of an effective one component plasma is used to quantify the overcorrelation of the light element induced by the admixture of a heavy element.

Free-energy functional of the Debye-Hückel model of simple fluids

The Debye-Hückel approximation to the free energy of a simple fluid is written as a functional of the pair correlation function. This functional can be seen as the Debye-Hückel equivalent to the functional derived in the hypernetted chain framework by Morita and Hiroike, as well as by Lado. It allows one to obtain the Debye-Hückel integral equation through a minimization with respect to the pair correlation function, leads to the correct form of the internal energy, and fulfills the virial theorem.

Transport properties of an asymmetric mixture in the dense plasma regime

We study how concentration changes ionic transport properties along isobars-isotherms for a mixture of hydrogen and silver, representative of turbulent layers relevant to inertial confinement fusion and astrophysics. Hydrogen will typically be fully ionized while silver will be only partially ionized but can have a large effective charge. This will lead to very different physical conditions for the H and Ag. Large first principles orbital free molecular dynamics simulations are performed and the resulting transport properties are analyzed. Comparisons are made with transport theory in the kinetic regime and in the coupled regime. The addition of a small amount of heavy element in a light material has a dramatic effect on viscosity and diffusion of the mixture. This effect is explained through kinetic theory as a manifestation of a crossover between classical diffusion and Lorentz diffusion.

Predictions of x-ray scattering spectra for warm dense matter

We present calculations of x-ray scattering spectra based on ionic and electronic structure factors that are computed from a new model for warm dense matter. In this model, which has no free parameters, the ionic structure is determined consistently with the electronic structure of the bound and free states. The x-ray scattering spectrum is thus fully determined by the plasma temperature, density and nuclear charge, and the experimental parameters. The combined model of warm dense matter and of the x-ray scattering theory is validated against an experiment on room-temperature, solid beryllium. It is then applied to experiments on warm dense beryllium and aluminum. Generally good agreement is found with the experiments. However, some significant discrepancies are revealed and appraised. Based on the strength of our model, we discuss the current state of x-ray scattering experiments on warm dense matter and their potential to determine plasma parameters, to discriminate among models, and to reveal interesting and difficult to model physics in dense plasmas.

Electronic and ionic structures of warm and hot dense matter

The results of a numerical implementation of the recent average atom model including ion-ion correlations of Starrett and Saumon [Phys. Rev. E 85, 026403 (2012)] are presented. The solution is obtained by coupling an average atom model to a two-component plasma model of electrons and ions. The two models are solved self-consistently and results are given in the form of pair distribution functions. Ion-ion pair distribution functions for hydrogen, carbon, aluminum, and iron are compared to quantum and Thomas-Fermi molecular dynamics simulations as well as path-integral Monte Carlo calculations and good agreement is found for a wide variety of plasma conditions in the warm and hot dense matter regime.