Wigner function quantum molecular dynamics

Classical molecular dynamics (MD) is a well established and powerful tool in various fields of science, e.g. chemistry, plasma physics, cluster physics and condensed matter physics. Objects of investigation are few-body systems and many-body systems as well. The broadness and level of sophistication of this technique is documented in many monographs and reviews, see for example \cite{Allan,Frenkel,mdhere}. Here we discuss the extension of MD to quantum systems (QMD). There have been many attempts in this direction which differ from one another, depending on the type of system under consideration. One direction of QMD has been developed for condensed matter systems and will not discussed here, e.g. \cite{fermid}. In this chapter we are dealing with unbound electrons as they occur in gases, fluids or plasmas. Here, one strategy is to replace classical point particles by wave packets, e.g. \cite{fermid,KTR94,zwicknagel06} which is quite successful. At the same time, this method struggles with problems related to the dispersion of such a packet and difficulties to properly describe strong electron-ion interaction and bound state formation. We, therefore, avoid such restrictions and consider a completely general alternative approach. We start discussion of quantum dynamics from a general consideration of quantum distribution functions.Comment: 18 pages, based on lecture at Hareaus school on computational phyics, Greifswald, September 200

Structure of strongly coupled, multi-component plasmas

We investigate the short-range structure in strongly coupled fluidlike plasmas using the hypernetted chain approach generalized to multicomponent systems. Good agreement with numerical simulations validates this method for the parameters considered. We found a strong mutual impact on the spatial arrangement for systems with multiple ion species which is most clearly pronounced in the static structure factor. Quantum pseudopotentials were used to mimic diffraction and exchange effects in dense electron-ion systems. We demonstrate that the different kinds of pseudopotentials proposed lead to large differences in both the pair distributions and structure factors. Large discrepancies were also found in the predicted ion feature of the x-ray scattering signal, illustrating the need for comparison with full quantum calculations or experimental verification

Monte Carlo results for the hydrogen Hugoniot

We propose a theoretical Hugoniot obtained by combining results for the equation of state (EOS) from the Direct Path Integral Monte Carlo technique (DPIMC) and those from Reaction Ensemble Monte Carlo (REMC) simulations. The main idea of such proposal is based on the fact that DPMIC provides first-principle results for a wide range of densities and temperatures including the region of partially ionized plasmas. On the other hand, for lower temperatures where the formation of molecules becomes dominant, DPIMC simulations become cumbersome and inefficient. For this region it is possible to use accurate REMC simulations where bound states (molecules) are treated on the Born-Oppenheimer level using a binding potential calculated by Kolos and Wolniewicz. The remaining interaction is then reduced to the scattering between neutral particles which is reliably treated classically applying effective potentials. The resulting Hugoniot is located between the experimental values of Knudson {\textit{et al.}} \cite{1} and Collins {\textit{et al.}} \cite{2}.Comment: 10 pges, 2 figures, 2 table

Temperature-dependent quantum pair potentials and their application to dense partially ionized hydrogen plasmas

Extending our previous work \cite{filinov-etal.jpa03ik} we present a detailed discussion of accuracy and practical applications of finite-temperature pseudopotentials for two-component Coulomb systems. Different pseudopotentials are discussed: i) the diagonal Kelbg potential, ii) the off-diagonal Kelbg potential iii) the {\em improved} diagonal Kelbg potential, iv) an effective potential obtained with the Feynman-Kleinert variational principle v) the ``exact'' quantum pair potential derived from the two-particle density matrix. For the {\em improved} diagonal Kelbg potential a simple temperature dependent fit is derived which accurately reproduces the ``exact'' pair potential in the whole temperature range. The derived pseudopotentials are then used in path integral Monte Carlo (PIMC) and molecular dynamics (MD) simulations to obtain thermodynamical properties of strongly coupled hydrogen. It is demonstrated that classical MD simulations with spin-dependent interaction potentials for the electrons allow for an accurate description of the internal energy of hydrogen in the difficult regime of partial ionization down to the temperatures of about $60 000$ K. Finally, we point out an interesting relation between the quantum potentials and effective potentials used in density functional theory.Comment: 18 pages, 11 figure

Dynamical Properties and Plasmon Dispersion of a Weakly Degenerate Correlated One-Component Plasma

Classical Molecular Dynamics (MD) simulations for a one-component plasma (OCP) are presented. Quantum effects are included in the form of the Kelbg potential. Results for the dynamical structure factor are compared with the Vlasov and RPA (random phase approximation) theories. The influence of the coupling parameter $\Gamma$, degeneracy parameter $\rho \Lambda^3$ and the form of the pair interaction on the optical plasmon dispersion is investigated. An improved analytical approximation for the dispersion of Langmuir waves is presented.Comment: 23 pages, includes 7 ps/eps-figures and 2 table

Thermodynamics of hot dense H-plasmas: Path integral Monte Carlo simulations and analytical approximations

This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pressure region between $10^{-1}$ and $10^2$ Mbar. In particular we present for this region results of extensive calculations based on a recently developed path integral Monte Carlo scheme (direct PIMC). This method allows for a correct treatment of the thermodynamic properties of hot dense Coulomb systems. Calculations were performed in a broad region of the nonideality parameter $\Gamma \lesssim 3$ and degeneracy parameter $n_e \Lambda^3 \lesssim 10$. We give a comparison with a few available results from other path integral calculations (restricted PIMC) and with analytical calculations based on Pade approximations for strongly ionized plasmas. Good agreement between the results obtained from the three independent methods is found.Comment: RevTex file, 21 pages, 5 ps-figures include

Interacting electrons in a one-dimensional random array of scatterers - A Quantum Dynamics and Monte-Carlo study

The quantum dynamics of an ensemble of interacting electrons in an array of random scatterers is treated using a new numerical approach for the calculation of average values of quantum operators and time correlation functions in the Wigner representation. The Fourier transform of the product of matrix elements of the dynamic propagators obeys an integral Wigner-Liouville-type equation. Initial conditions for this equation are given by the Fourier transform of the Wiener path integral representation of the matrix elements of the propagators at the chosen initial times. This approach combines both molecular dynamics and Monte Carlo methods and computes numerical traces and spectra of the relevant dynamical quantities such as momentum-momentum correlation functions and spatial dispersions. Considering as an application a system with fixed scatterers, the results clearly demonstrate that the many-particle interaction between the electrons leads to an enhancement of the conductivity and spatial dispersion compared to the noninteracting case.Comment: 10 pages and 8 figures, to appear in PRB April 1

Phase Transition in Strongly Degenerate Hydrogen Plasma

Direct fermionic path-integral Monte-Carlo simulations of strongly coupled hydrogen are presented. Our results show evidence for the hypothetical plasma phase transition. Its most remarkable manifestation is the appearance of metallic droplets which are predicted to be crucial for the electrical conductivity allowing to explain the rapid increase observed in recent shock compression measurments.Comment: 1 LaTeX file using jetpl.cls (included), 5 ps figures. Manuscript submitted to JETP Letter

Quasi-classical Molecular Dynamics Simulations of the Electron Gas: Dynamic properties

Results of quasi-classical molecular dynamics simulations of the quantum electron gas are reported. Quantum effects corresponding to the Pauli and the Heisenberg principle are modeled by an effective momentum-dependent Hamiltonian. The velocity autocorrelation functions and the dynamic structure factors have been computed. A comparison with theoretical predictions was performed.Comment: 8 figure

Smearing Formula for Higher-Order Effective Classical Potentials

In the variational approach to quantum statistics, a smearing formula describes efficiently the consequences of quantum fluctuations upon an interaction potential. The result is an effective classical potential from which the partition function can be obtained by a simple integral. In this work, the smearing formula is extended to higher orders in the variational perturbation theory. An application to the singular Coulomb potential exhibits the same fast convergence with increasing orders that has been observed in previous variational perturbation expansions of the anharmonic oscillator with quartic potential.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re267/preprint.htm