arXiv subjects

Lee A. Collins

Publications and source records attributed to Lee A. Collins.

14 recordsLinked to original sources

arXiv2025

Mixed Stochastic-Deterministic Density Functional Theoretic Decomposition of Kubo-Greenwood Conductivities in the Projector Augmented Wave Formalism

Pairing the accuracy of Kohn-Sham density-functional framework with the efficiency of a stochastic algorithmic approach, mixed stochastic-deterministic Density Functional Theory (mDFT) achieves a favorable computational scaling with system sizes and electronic temperatures. We employ the recently developed mDFT formalism to investigate the dynamic charge-transport properties of systems in the warm dense matter regime. The optical conductivity spectra are computed for single- and multi- component mixtures of carbon, hydrogen, and beryllium using two complementary approaches: Kubo-Greenwood in the mDFT picture and real-time Time-Dependent mDFT. We further devise a decomposition of the Onsager coefficients leading up to the Kubo-Greenwood spectra to exhibit contributions from the deterministic, stochastic, and mixed electronic state transitions at different incident photon energies.

physics.chem-ph↗

arXiv2024

Optical and Transport Properties of Plasma Mixtures from Ab Initio Molecular Dynamics

Predicting the charged particle transport properties of warm dense matter / hot dense plasma mixtures is a challenge for analytical models. High accuracy ab initio methods are more computationally expensive, but can provide critical insight by explicitly simulating mixtures. In this work, we investigate the transport properties and optical response of warm dense carbon-hydrogen mixtures at varying concentrations under either conserved electronic pressure or mass density at a constant temperature. We compare options for mixing the calculated pure species properties to estimate the results of the mixtures. We find that a combination of the Drude model with the Matthiessen's rule works well for DC electron transport and low frequency optical response. This breaks down at higher frequencies, where a volumetric mix of pure-species AC conductivities works better.

physics.plasm-ph↗

arXiv2023

High-order finite element method for atomic structure calculations

We introduce \texttt{featom}, an open source code that implements a high-order finite element solver for the radial Schrödinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or exponential, and the convergence can be systematically controlled by increasing the number and/or polynomial order of the finite element basis functions. The Dirac equation is solved using a squared Hamiltonian approach to eliminate spurious states. To address the slow convergence of the $κ=\pm1$ states due to divergent derivatives at the origin, we incorporate known asymptotic forms into the solutions. We achieve a high level of accuracy ($10^{-8}$ Hartree) for total energies and eigenvalues of heavy atoms such as uranium in both Schrödinger and Dirac Kohn-Sham solutions. We provide detailed convergence studies and computational parameters required to attain commonly required accuracies. Finally, we compare our results with known analytic results as well as the results of other methods. In particular, we calculate benchmark results for atomic numbers ($Z$) from 1 to 92, verifying current benchmarks. We demonstrate significant speedup compared to the state-of-the-art shooting solver \texttt{dftatom}. An efficient, modular Fortran 2008 implementation, is provided under an open source, permissive license, including examples and tests, wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.

physics.atom-ph↗

arXiv2023

Stochastic and Mixed Density Functional Theory within the projector augmented wave formalism for the simulation of warm dense matter

Stochastic and mixed stochastic-deterministic density functional theory (DFT) are promising new approaches for the calculation of the equation-of-state and transport properties in materials under extreme conditions. In the intermediate warm dense matter regime, a state between correlated condensed matter and kinetic plasma, electrons can range from being highly localized around nuclei to delocalized over the whole simulation cell. The plane-wave basis pseudo-potential approach is thus the typical tool of choice for modeling such systems at the DFT level. Unfortunately, the stochastic DFT methods scale as the square of the maximum plane-wave energy in this basis. To reduce the effect of this scaling, and improve the overall description of the electrons within the pseudo-potential approximation, we present stochastic and mixed DFT developed and implemented within the projector augmented wave formalism. We compare results between the different DFT approaches for both single-point and molecular dynamics trajectories and present calculations of self-diffusion coefficients of solid density carbon from 1 to 50 eV.

physics.comp-ph↗

arXiv2021

Mixed Stochastic-Deterministic Time-Dependent Density Functional Theory: Application to Stopping Power of Warm Dense Carbon

Warm dense matter (WMD) describes an intermediate phase, between condensed matter and classical plasmas, found in natural and man-made systems. In a laboratory setting, WDM needs to be created dynamically. It is typically laser or pulse-power generated and can be difficult to characterize experimentally. Measuring the energy loss of high energy ions, caused by a WDM target, is both a promising diagnostic and of fundamental importance to inertial confinement fusion research. However, electron coupling, degeneracy, and quantum effects limit the accuracy of easily calculable kinetic models for stopping power, while high temperatures make the traditional tools of condensed matter, e.g. Time-Dependent Density Functional Theory (TD-DFT), often intractable. We have developed a mixed stochastic-deterministic approach to TD-DFT which provides more efficient computation while maintaining the required precision for model discrimination. Recently, this approach showed significant improvement compared to models when compared to experimental energy loss measurements in WDM carbon. Here, we describe this approach and demonstrate its application to warm dense carbon stopping acr

physics.plasm-ph↗

arXiv2020

Fast and Universal Kohn Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma

Understanding many processes, e.g. fusion experiments, planetary interiors and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter (WDM) and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly-free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive \emph{ab initio} atomistic computation, typically based on quantum mechanical Kohn-Sham Density Functional Theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the WDM regime. A recently-developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (<50 eV). We have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.

physics.comp-ph↗

arXiv2020

Static and dynamic properties of multi-ionic plasma mixtures

Complex plasma mixtures with three or more components are often encountered in astrophysics or in inertial confinement fusion (ICF) experiments. For mixtures containing species with large differences in atomic number Z, the modeling needs to consider at the same time the kinetic theory for low-Z elements combined with the theory of strongly coupled plasma for high-Z elements, as well as all the intermediate situations that can appear in multi-component systems. For such cases, we study the pair distribution functions, self-diffusions, mutual diffusion and viscosity for ternary mixtures at extreme conditions. These quantities can be produced from first principles using orbital free molecular dynamics at the computational expense of very intensive simulations to reach good statistics. Utilizing the first-principles results as reference data, we assess the merit of a global analytic model for transport coefficients, Pseudo-Ions in Jellium (PIJ), based on an iso-electronic assumption ( iso-n e ). With a multi-component hypernetted-chain integral equation, we verify the quality of the iso-n e prescription for describing the static structure of the mixtures. This semi-analytical modeling compares well with the simulation results and allows one to consider plasma mixtures not accessible to simulations. Applications are given for the mix of materials in ICF experiments. A reduction of a multicomponent mixture to an effective binary mixture is also established in the hydrodynamic limit and compared with PIJ estimations for ICF relevant mixtures.

physics.plasm-ph↗

arXiv2018

Checking the Salpeter enhancement of nuclear reactions in asymmetric mixtures

We investigate the plasma enhancement of nuclear reactions in the intermediate coupling regime using orbital free molecular dynamics (OFMD) simulations. Mixtures of H-Cu and H-Ag serve as prototypes of simultaneous weak and strong couplings due to the charge asymmetry. Of particular importance is the partial ionization of Cu and Ag and the free electron polarization captured by OFMD simulations. By comparing a series of OFMD simulations at various concentrations and constant pressure to multi-component hyper netted chain (MCHNC) calculations of effective binary ionic mixtures (BIM), we set a general procedure for computing enhancement factors. The MCHNC procedure allows extension to very low concentrations (5% or less) and to very high temperatures (few keV) unreachable by the simulations. Enhancement factors for nuclear reactions rates extracted from the MCHNC approach are compared with the Salpeter theory in the weak and strong coupling regimes, and a new interpolation is proposed.

physics.plasm-ph↗

arXiv2017

Planetary Ices and the Linear Mixing Approximation

The validity of the widely used linear mixing approximation for the equations of state (EOS) of planetary ices is investigated at pressure-temperature conditions typical for the interior of Uranus and Neptune. The basis of this study are ab initio data ranging up to 1000 GPa and 20 000 K calculated via density functional theory molecular dynamics simulations. In particular, we calculate a new EOS for methane and EOS data for the 1:1 binary mixtures of methane, ammonia, and water, as well as their 2:1:4 ternary mixture. Additionally, the self-diffusion coefficients in the ternary mixture are calculated along three different Uranus interior profiles and compared to the values of the pure compounds. We find that deviations of the linear mixing approximation from the results of the real mixture are generally small; for the thermal EOS they amount to 4% or less. The diffusion coefficients in the mixture agree with those of the pure compounds within 20% or better. Finally, a new adiabatic model of Uranus with an inner layer of almost pure ices is developed. The model is consistent with the gravity field data and results in a rather cold interior ($\mathrm{T_{core}} \mathtt{\sim}$ 4000 K).

astro-ph.EP↗

arXiv2016

A unified concept of effective one component plasma for hot dense plasmas

Orbital-free molecular dynamics simulations are used to benchmark two popular models for hot dense plasmas: the one component plasma (OCP) and the Yukawa model. A unified concept emerges where an effective OCP (eOCP) is constructed from the short-range structure of the plasma. An unambiguous ionization and the screening length can be defined and used for a Yukawa system, which reproduces the long range structure with finite compressibility. Similarly, the dispersion relation of longitudinal waves is consistent with the screened model at vanishing wavenumber but merges with the OCP at high wavenumber. Additionally, the eOCP reproduces the overall relaxation timescales of the correlation functions associated with ionic motion. In the hot dense regime, this unified concept of eOCP can be fruitfully applied to deduce properties such as the equation of state, ionic transport coefficients, and the ion feature in x-ray Thomson scattering experiments.

physics.plasm-ph↗

arXiv2013

Elastic scattering of a Bose-Einstein condensate at a potential landscape

We investigate the elastic scattering of Bose-Einstein condensates at shallow periodic and disorder potentials. We show that the collective scattering of the macroscopic quantum object couples to internal degrees of freedom of the Bose-Einstein condensate such that the Bose-Einstein condensate gets depleted. As a precursor for the excitation of the Bose-Einstein condensate we observe wave chaos within a mean-field theory.

cond-mat.quant-gas↗

arXiv2013

Critical velocity for a toroidal Bose-Einstein condensate flowing through a barrier

We consider the setup employed in a recent experiment (Ramanathan et al 2011 Phys. Rev. Lett. 106 130401) devoted to the study of the instability of the superfluid flow of a toroidal Bose-Einstein condensate in presence of a repulsive optical barrier. Using the Gross-Pitaevskii mean-field equation, we observe, consistently with what we found in Piazza et al (2009 Phys. Rev. A 80 021601), that the superflow with one unit of angular momentum becomes unstable at a critical strength of the barrier, and decays through the mechanism of phase slippage performed by pairs of vortex-antivortex lines annihilating. While this picture qualitatively agrees with the experimental findings, the measured critical barrier height is not very well reproduced by the Gross-Pitaevskii equation, indicating that thermal fluctuations can play an important role (Mathey et al 2012 arXiv:1207.0501). As an alternative explanation of the discrepancy, we consider the effect of the finite resolution of the imaging system. At the critical point, the superfluid velocity in the vicinity of the obstacle is always of the order of the sound speed in that region, $v_{\rm barr}=c_{\rm l}$. In particular, in the hydrodynamic regime (not reached in the above experiment), the critical point is determined by applying the Landau criterion inside the barrier region. On the other hand, the Feynman critical velocity $v_{\rm f}$ is much lower than the observed critical velocity. We argue that this is a general feature of the Gross-Pitaevskii equation, where we have $v_{\rm f}=ε c_{\rm l}$ with $ε$ being a small parameter of the model. Given these observations, the question still remains open about the nature of the superfluid instability.

cond-mat.quant-gas↗

arXiv2009

Electron correlation in two-photon double ionization of helium from attosecond to FEL pulses

We investigate the role of electron correlation in the two-photon double ionization of helium for ultrashort XUV pulses with durations ranging from a hundred attoseconds to a few femtoseconds. We perform time-dependent ab initio calculations for pulses with mean frequencies in the so-called "sequential" regime (photon energy above 54.4 eV). Electron correlation induced by the time correlation between emission events manifests itself in the angular distribution of the ejected electrons, which strongly depends on the energy sharing between them. We show that for ultrashort pulses two-photon double ionization probabilities scale non-uniformly with pulse duration depending on the energy sharing between the electrons. Most interestingly we find evidence for an interference between direct ("nonsequential") and indirect ("sequential") double photo-ionization with intermediate shake-up states, the strength of which is controlled by the pulse duration. This observation may provide a route toward measuring the pulse duration of FEL pulses.

physics.atom-ph↗

arXiv2007

Parallel TREE code for two-component ultracold plasma analysis

The TREE method has been widely used for long-range interaction {\it N}-body problems. We have developed a parallel TREE code for two-component classical plasmas with open boundary conditions and highly non-uniform charge distributions. The program efficiently handles millions of particles evolved over long relaxation times requiring millions of time steps. Appropriate domain decomposition and dynamic data management were employed, and large-scale parallel processing was achieved using an intermediate level of granularity of domain decomposition and ghost TREE communication. Even though the computational load is not fully distributed in fine grains, high parallel efficiency was achieved for ultracold plasma systems of charged particles. As an application, we performed simulations of an ultracold neutral plasma with a half million particles and a half million time steps. For the long temporal trajectories of relaxation between heavy ions and light electrons, large configurations of ultracold plasmas can now be investigated, which was not possible in past studies.

physics.comp-ph↗