Variational Formulation of Time-Dependent Density Functional Theory

We present a variational formulation of Time-Dependent Density Functional Theory similar to the constrained-search variational formulation of ground-state density-function theory. The formulation is applied to justify the time-dependent Kohn-Sham method. Other promising applications to advance TDDFT are suggested.Comment: 5 page

Correlation Effects on the Temperature Relaxation Rates in Dense Plasmas

We present a model for the rate of temperature relaxation between electrons and ions in plasmas. The model includes self-consistently the effects of particle screening, electron degeneracy and correlations between electrons and ions. We successfully validate the model over a wide range of plasma coupling against molecular-dynamics simulations of classical plasma of like-charged electrons and ions. We present calculations of the relaxation rates in dense hydrogen and show that, while electron-ion correlation effects are indispensable in classical, like-charged plasmas at any density and temperature, quantum diffraction effects prevail over e-i correlation effects in dense hydrogen plasmas.Comment: 14 pages, 9 figure

First-Principles Determination of Electron-Ion Couplings in the Warm Dense Matter Regime

We present first-principles calculations of the rate of energy exchanges between electrons and ions in nonequilibrium warm dense plasmas, liquid metals and hot solids, a fundamental property for which various models offer diverging predictions. To this end, a Kubo relation for the electron-ion coupling parameter is introduced, which includes self-consistently the quantum, thermal, non-linear and strong coupling effects that coexist in materials at the confluence of solids and plasmas. Most importantly, like other Kubo relations widely used for calculating electronic conductivities, the expression can be evaluated using quantum molecular dynamics simulations. Results are presented and compared to experimental and theoretical predictions for representative materials of various electronic complexity, including aluminum, copper, iron and nickel

Non-Adiabatic Quantum Molecular Dynamics with Detailed Balance

We present an approach for carrying out non-adiabatic molecular dynamics simulations of systems in which non-adiabatic transitions arise from the coupling between the classical atomic motions and a quasi-continuum of electronic quantum states. Such conditions occur in many research areas, including chemistry at metal surfaces, radiation damage of materials, and warm dense matter physics. The classical atomic motions are governed by stochastic Langevin-like equations, while the quantum electron dynamics is described by a master equation for the populations of the electronic states. These working equations are obtained from a first-principle derivation. Remarkably, unlike the widely used Ehrenfest and surface-hopping methods, the approach naturally satisfies the principle of detailed balance at equilibrium and, therefore, can describe the evolution to thermal equilibrium from an arbitrary initial state. In addition, unlike other schemes, there is no need to explicitly propagate wave functions in time.Comment: 5 pages, 0 figure, to be submitte

Transport Regimes Spanning Magnetization-Coupling Phase Space

The manner in which transport properties vary over the entire parameter-space of coupling and magnetization strength is explored for the first time. Four regimes are identified based on the relative size of the gyroradius compared to other fundamental length scales: the collision mean free path, Debye length, distance of closest approach and interparticle spacing. Molecular dynamics simulations of self-diffusion and temperature anisotropy relaxation spanning the parameter space are found to agree well with the predicted boundaries. Comparison with existing theories reveals regimes where they succeed, where they fail, and where no theory has yet been developed.Comment: 10 pages, 4 figure

Fast and accurate quantum molecular dynamics of dense plasmas across temperature regimes

We have developed and implemented a new quantum molecular dynamics approximation that allows fast and accurate simulations of dense plasmas from cold to hot conditions. The method is based on a carefully designed orbital-free implementation of density functional theory (DFT). The results for hydrogen and aluminum are in very good agreement with Kohn-Sham (orbital-based) DFT and path integral Monte Carlo (PIMC) for microscopic features such as the electron density as well as equation of state. The present approach does not scale with temperature and hence extends to higher temperatures than is accessible in Kohn-Sham method and lower temperatures than is accessible by PIMC, while being significantly less computationally expensive than either of those two methodsComment: 7 page

Modified Enskog Kinetic Theory for Strongly Coupled Plasmas

Concepts underlying the Enskog kinetic theory of hard-spheres are applied to include short-range correlation effects in a model for transport coefficients of strongly coupled plasmas. The approach is based on an extension of the effective potential transport theory [S.~D.~Baalrud and J.~Daligault, Phys.~Rev.~Lett.~{\bf 110}, 235001 (2013)] to include an exclusion radius surrounding individual charged particles that is associated with Coulomb repulsion. This is obtained by analogy with the finite size of hard spheres in Enskog's theory. Predictions for the self-diffusion and shear viscosity coefficients of the one-component plasma are tested against molecular dynamics simulations. The theory is found to accurately capture the kinetic contributions to the transport coefficients, but not the potential contributions that arise at very strong coupling ($\Gamma \gtrsim 30$). Considerations related to a first-principles generalization of Enskog's kinetic equation to continuous potentials are also discussed.Comment: 12 pages, 11 figure

Mean Force Kinetic Theory: a Convergent Kinetic Theory for Weakly and Strongly Coupled Plasmas

A new closure of the BBGKY hierarchy is developed, which results in a convergent kinetic equation that provides a rigorous extension of plasma kinetic theory into the regime of strong Coulomb coupling. The approach is based on a single expansion parameter which enforces that the exact equilibrium limit is maintained at all orders. Because the expansion parameter does not explicitly depend on the range or the strength of the interaction potential, the resulting kinetic theory does not suffer from the typical divergences at short and long length scales encountered when applying the standard kinetic equations to Coulomb interactions. The approach demonstrates that particles effectively interact via the potential of mean force and that the range of this force determines the size of the collision volume. When applied to a plasma, the collision operator is shown to be related to the effective potential theory [Baalrud and Daligault, Phys. Rev. Lett 110, 235001 (2013)]. The relationship between this and previous kinetic theories is discussed.Comment: 12 page

Gradient corrections to the exchange-correlation free energy

We develop the first order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite temperature density functional calculations. Based on this we propose and implement a simple temperature dependent extension for functionals beyond the local density approximation. These finite temperature functionals show improvement over zero temperature functionals as compared to path integral Monte Carlo calculations for deuterium and perform without computational cost increase compared to zero temperature functionals and so should be used for finite temperature calculations

Temperature Anisotropy Relaxation of the One-Component Plasma

The relaxation rate of a Maxwellian velocity distribution function that has an initially anisotropic temperature $(T_\parallel \neq T_\perp)$ is an important physical process in space and laboratory plasmas. It is also a canonical example of an energy transport process that can be used to test theory. Here, this rate is evaluated using molecular dynamics simulations of the one-component plasma. Results are compared with the predictions of four kinetic theories; two treating the weakly coupled regime (1) the Landau equation, and (2) the Lenard-Balescu equation, and two that attempt to extend the theory into the strongly coupled regime (3) the effective potential theory and (4) the generalized Lenard-Balescu theory. The role of dynamic screening is studied, and is found to have a negligible influence on this transport rate. Oscillations and a delayed relaxation onset in the temperature profiles are observed at strong coupling, which are not described by the kinetic theories.Comment: 15 pages, 7 figures, to be published in Contributions to Plasma Physic