Topic/Type: 1.5 Low-temperature, dusty and nano-plasmas, Poster

### Path integral Monte Carlo simulations of the strongly coupled Coulomb systems.

V. S. Filinov1, M. Bonitz2, P.R. Levashov1, Y.B. Ivanov3, 4, V.V. Skokov3, 5, V.E. Fortov1

1 Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13/19, Moscow 125412, Russia
2 Institute for Theoretical Physics and Astrophysics, Leibnizstrasse 15, D-24098 Kiel, Germany
3 Gesellschaft fur Schwerionenforschung, Planckstrasse 1, D-64291 Darmstadt, Germany
4 Russian Research Center ''Kurchatov Institute'', Kurchatov Sq. 1, 123182 Moscow, Russia
5 Bogoliubov Lab. of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Russia

There exist many strongly correlated Coulomb systems where quantum and statistical effects are important. Examples are dense astrophysical plasmas in the interior of giant planets or white dwarf stars as well as quark -- gluon plasma, electron-hole (e-h) plasmas in condensed matter, few-particle electron or exciton clusters in mesoscopic quantum dots and so on. The formation of Coulomb bound states, of Coulomb liquids and electron-hole droplets are examples of the large variety of correlation phenomena in these systems.

Here we present results for 3D hydrogen, e -- h and quark -- gluon plasmas in the wide region of temperature, density and charges mass ratio. Our calculations include region of appearance and decay of
the bound state, Mott transition from neutral plasma to metallic--like clusters, formation from clusters the hexatic -- like liquid (for 2D case) and then formation of the crystal -- like lattice and at very low temperatures transition of this 'latice' to antiferromagnetic structure.

In our studies we use the direct quantum path integral Monte Carlo method developed for studying strongly correlated plasma media at finite temperature. In contrast to hydrogen (and similar) plasmas, in quark -- gluon and e -- h plasmas the heavy component has to be treated quantum mechanically. A second extension beyond our previous simulations is an improved treatment of exchange which allows us to reach higher densities and lower temperatures required to study the Mott effect and heavy charges crystallization. Developed approach allows to do calculations of thermodynamic properties. Internal energy, pressure and pair correlation functions have been obtained in wide range of density and temperatures. A strongly coupled plasma of quark and gluon quasiparticles at temperatures from $\small 1.1 T_c$ to $\small 3 T_c$ is studied by path integral Monte Carlo simulations. This method extends previous classical nonrelativistic simulations based on a color Coulomb interaction to the quantum regime. We present the equation of state and find good agreement with exact but very difficult lattice calculations. Pair distribution functions and color correlation functions are computed indicating strong correlations and liquid-like behavior.

We present also the 'straight generalization' of classical molecular dynamics methods for rigorous consideration of the dynamic quantum problems. The words 'straight generalization' mean that in classical limit the developed approach exactly coincides with molecular dynamics method in the phase space. A generalization molecular dynamics method is possible only in the phase space, so it is naturally to use Wigner formulation of quantum mechanics. The numerical procedure combining both molecular dynamics and Monte Carlo methods for solving the integral Wigner- Liouville equation has been applied to the treatment of kinetic properties of quantum dense hydrogen plasma. To study the influence of the Coulomb interaction on kinetic properties of dense plasma we have simulated the quantum dynamics in a canonical ensemble at finite temperature for both weakly and strongly coupled plasmas. The main quantities are the temporal momentum-momentum correlation functions and their frequency-domain Fourier transforms. We discovered that the temporal momentum-momentum correlation functions and their frequency-domain Fourier transforms strongly depend on the plasma coupling parameter. For low density and high temperatures numerical results agree well with Drude approximation and Silin, Rukhadze formula. Growth of coupling parameter results in strong deviation the frequency dependent conductivity and permittivity from low density and high temperature approximations.