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A generalization of the “single-momentum” approach to the calculation of the Wigner function of a quantum canonical ensemble is made. A Monte Carlo method is developed for calculating the thermodynamic properties of multicomponent fermion systems. The momentum distribution functions, the internal energy, the equation of state, and the pair-correlation functions of hydrogen plasma under the conditions of strong nonideality and moderate degeneracy are calculated.

In the framework of the statistical theory of liquids, the thermodynamic parameters of a strongly nonideal Coulomb microparticle structure confined in a Paul linear trap in atmospheric-pressure air are calculated using the Brownian dynamics method. The Coulomb potential of interparticle interaction and the calculated pair correlation functions of the Coulomb structure are used in calculations. The average interparticle interaction parameter (the coupling parameter Γ), the internal energy of the Coulomb structure, and the pressure it imposes on the trap are calculated. It has been found that the parameters mentioned above decrease with increasing size and charge of particles due to an increase in the average equilibrium interparticle distance in the electrodynamic trap. As the system approaches a steady state, the energy and pressure also decrease due to an increase in the average interparticle distance caused by a partial ordering of the Coulomb system of particles.

The new {\em ab initio} quantum path integral Monte Carlo approach has been developed and applied for the entropy difference calculations for the strongly coupled degenerated uniform electron gas (UEG), a well--known model of simple metals. Calculations have been carried out at finite temperature in canonical ensemble over the wide density and temperature ranges. Obtained data may be crucial for density functional theory. Improvements of the developed approach include the Coulomb and exchange interaction of fermions in the basic Monte Carlo cell and its periodic images and the proper change of variables in the path integral measure. The developed approach shows good agreement with available results for fermions even at temperature four times less than the Fermi energy and practically doesn't suffer from the "fermionic sign problem", which takes place in standard path integral Monte Carlo simulations of degenerate fermionic systems. Presented results include pair distribution functions, isochors and isotherms of pressure, internal energy and entropy change in strongly coupled and degenerate UEG in a wide range of density and temperature., 8 pages, 2 figures

In this paper we study thermodynamic properties of uniform electron gas (UEG) over wide density and temperature range, using the improved fermionic-path-integral Monte Carlo (FPIMC) method. This method demonstrates a significant reduction of the "fermionic sign problem," which takes place in standard path-integral Monte Carlo simulations of degenerate fermionic systems. We introduce three basic improvements. The first one is the improved treatment of exchange interaction, achieved by the proper change of variables in the path-integral measure. The second improvement is the inclusion of long-range Coulomb effects into an angle-averaged effective potential, as proposed by Yakub and Ronchi [J. Chem. Phys. 119, 11556 (2003)JCPSA60021-960610.1063/1.1624364]. The third improvement is the angle-averaging of an exchange determinant, describing the fermionic exchange interaction not only between particles in the main Monte Carlo cell, but also with electrons in the nearest periodic images. The FPIMC shows very good agreement with analytical data for ideal Fermi gas. For strongly coupled UEG under warm dense matter conditions we compare our total and exchange-correlation energy results with other Monte Carlo approaches.

An explicit analytical expression of the Wigner function has been proposed to account for Fermi statistical effects using an effective pair pseudopotential in phase space. The derived pseudopotential depends on coordinates, momenta, and the degeneracy parameter of fermions and takes into account Pauli blocking of fermions in phase space. A new quantum Monte Carlo method (WPIMC) is put forward to calculate average values of arbitrary quantum operators in phase space. When calculated using the WPIMC method, the momentum distributions and pair distribution functions for degenerate ideal fermions are in good agreement with the analytical distribution over a wide range of values of the degeneracy parameter. Generalization of this approach for treating strongly correlated fermions is in progress.

Quantum effects can affect the shape of the particle kinetic energy distribution function, as the interaction of a particle with its surroundings restricts the volume of configuration space, which, due to the uncertainty relation, results in an increase in the volume of the momentum space, i.e., in a rise in the fraction of particles with higher momenta. Allowing for quantum effects at calculations of the equilibrium rate constants of inelastic processes is important in consideration of such phenomena as the transition of combustion into detonation, flame propagation, vibrational relaxation, and even thermonuclear fusion at high pressure and low temperatures. Quantum effects are also important in treatment of transport properties of the strongly interacting systems of many particles. In this work the new path integral representation of the quantum Wigner function in the phase space has been developed for canonical ensemble. Explicit analytical expression of the Wigner function has been obtained in harmonic approximation. New quantum Monte-Carlo method for ab initio calculations of the average values of quantum operators, Wigner function, momentum and position distributions and wave functions of the ground state has been developed and tested. Obtained results are in a very good agreement with available analytical results and results of usual path-integral Monte-Carlo method. The developed approach allows simulation of thermodynamic and kinetic properties of quantum systems and calculation average values of quantum operators, when the usual path integral Monte Carlo methods in configurational space failed. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Based on the constituent quasiparticle model of the quark-gluon plasma (QGP), color quantum path-integral Monte-Carlo (PIMC) calculations of the thermodynamic properties of the QGP are performed. We extend our previous zero chemical potential simulations to the QGP at finite baryon chemical potential. The results indicate that color PIMC can be applied not only above the QCD critical temperature Tc but also below Tc. Besides reproducing the lattice equation of state our approach yields also valuable additional insight into the internal structure of the QGP, via the pair distribution functions of the various quasiparticles. In particular, the pair distribution function of gluons reflects the existence of gluon-gluon bound states at low temperatures and μ = 175 MeV, i.e. glueballs, while meson-like bound states are not found. (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The conditions of capture and retention of charged dust particles in linear Paul traps in air at atmospheric pressure in a wide range of parameters characterizing both dynamic traps and confined particles have been found by means of Brownian dynamics. It is shown that the viscosity of a gaseous medium strongly affects capture and retention of dust particles. The simulation results are in agreement with the experimental data on the creation and retention of a stable Coulomb cluster of charged dust particles in a quadrupole trap.

The new numerical version of the Wigner approach to quantum mechanics for treatment thermodynamic properties of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations obtained in different kind of perturbation theories can not be applied. Explicit analytical expression of the Wigner function has been obtained in linear and harmonic approximations. Fermi statistical effects are accounted by effective pair pseudopotential depending on coordinates, momenta and degeneracy parameter of particles and taking into account Pauli blocking of fermions. The new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been proposed. Calculations of the momentum distribution function of the degenerate ideal Fermi gas have been carried out for testing the developed approach. Comparison of obtained momentum distribution function of strongly correlated Coulomb systems of particles with Maxwell -- Boltzmann and Fermi distributions shows the significant influence of interparticle interaction both at small momenta and in the high energy quantum 'tails'., Comment: 14 pages, 6 captured figures. arXiv admin note: text overlap with arXiv:1702.04091

Over the last decades the fixed-node method has been used for a numerical treatment of thermo-dynamic properties of strongly correlated Fermi systems. In this work correctness of the fixed-node method for ideal Fermi systems is analytically analyzed. It is shown that the fixed-node prescription of calculation of the density matrix leads to contradictions even for two ideal fermions. The main conclusion of this work is that the fixed-node method can not reproduce the fermion density matrices and should be considered as uncontrolled empirical approach in treatment of thermodynamics of Fermi systems.

The Wigner's pseudo-particle formalism has been generalized to describe quantum dynamics of relativistic particle in external potential field. As a simplest application of the developed formalism the time evolution of the 1D relativistic quantum harmonic oscillator been considered. Due to the complex structure of the evolution equation for Wigner function, the only numerical treatment is possible by combining Monte Carlo and molecular dynamics methods. Relativistic dynamics results in appearance of the new physical effects as opposed to non-relativistic case. Interesting is the complete changing of the shape of the momentum and coordinate distribution functions as well as formation of ‘unexpected’ protuberances. To analyze the influence of relativistic effects on average values of quantum operators, the dependencies on time of average momentum, position, their dispersions and energy have been compared for the non-relativistic and relativistic dynamics.

We are going to study the kinetic properties of dense hydrogen plasma by a new quantum dynamics method in the Wigner representation of quantum mechanics. This method combines the Feynman and Wigner formulation of quantum mechanics and uses for calculation the direct path integral Monte Carlo (PIMC) and molecular dynamics methods. We are going to solve the Wigner–Liouville equation for dense degenerate hydrogen with the initial condition sampled by the PIMC method from equilibrium plasma state. We hope to do calculations of the hydrogen plasma properties under extreme conditions.

Institute of Physics, University Greifswald, Felix-Hausdorff-Str. 6, D-17487 Greifswald, GermanyReceived 14 October 2011, revised 16 February 2012, accepted 23 February 2012Published online 11 April 2012Key words Strongly correlated two-component plasma, Coulomb crystallization.We perform a first-principle analysis of Coulomb crystallization in neutral two-component mass asymmetricplasmas by large-scale path integral Monte Carlo simulations for a dense hydrogen plasma in a broad densityrange. We observe two large jumps in the relative distance fluctuations of protons that are connected withqualitative changes in the behavior of the proton pair distribution function and are attributed to the formation ofa spatially ordered state. A third smaller jump inside the ordered phase indicates a structural transition.

A strongly coupled quark-gluon plasma (QGP) of constituent quasiparticles is studied by a path-integral Monte-Carlo method. This approach is a quantum generalization of the model developed by Gelman, Shuryak and Zahed. It is shown that this method is able to reproduce the QCD lattice equation of state, internal energy, entropy and trace anomaly (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Usually electrostatic fields created by electrodes of the trap are used for dust particle confinement in plasma devices. In this work the possibility of the dust particle confinement by electrodynamic fields is investigated for improved quadrupole traps. The behavior of dust particles is simulated by Brownian dynamics. Dust particle parameters and parameters of the traps needed for dust particle confinement have been obtained (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The results of investigations of dust grain behavior in plasma formed by a proton beam in inert gases (He, Ar, Kr) are demonstrated. Stable ordered dust structures, namely “a plasma-dust crystal” formed of dust grains 1.0, 3.0, and 4.8 μm in diameter are obtained in the proton beam range for the first time. The mathematical model which allows for numerical simulation of crystal formation from dust grains formed by proton beam plasma is developed.

A nuclear excited dusty plasma can be used effec� tively in systems of direct nuclear energy conversion, for example, into optical radiation energy. However, to compensate for gravity and to confine charged dust particles, a potential trap must be formed in a nuclear excited plasma. High pressures (1–100 atm) are needed to effectively use a nuclear excited plasma. Here, we investigate the possibility of using a corona electric discharge to provide the existence of dust structures before the action of hard radiation on a plasma–dust medium. The problem is considered in terms of continuum equations. We consider the case where a nuclear excited dusty plasma is in a cylinder of length L and radius R (L/R 1) with a wire of radius r 0 stretched through the center. The distributions of the number densities of electrons (ne), singly charged atomic (ni) and molecular (nmi) ions, excited atoms (n*), and metastable atoms (nam) and molecules (nMm) depend on the specific kinetics of elementary processes and the local electric field Er(r). These stationary distribu� tions can be found by simultaneously solving the par� ticle number balance equations

A method of the controlled effect by the electric fields on Coulomb structures in the linear electrodynamic trap for the controlled compression and stretching of these structures was proposed. The obtained images of the Coulomb structures at various frequencies of effect by rectangular pulses of the electric field are presented. Such effects can be used to obtain the thermodynamic properties of the Coulomb structures by the statistical method.

The highly ordered levitating structures of radioactive dusty particles in nuclear excited plasma oftube capacitor are studied using the Brownian dynamics. Models with potential and non potential forces acting on charged dusty particles have been investigated. Types and stability of obtained dust particle structures are analyzed at atmospheric pressure and normal conditions. The stationary crystal – like structures have been obtained only for potential forces acting on dusty particles, while in model with non potential forces the formation of two slowly rotating in opposite direction highly ordered vortices has been predicted (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to their numerical implementation. As test cases, we consider the time evolution of Gaussian wave packets in different one-dimensional geometries, whereby tunneling, resonance and anharmonicity effects are taken into account. The results and methods are benchmarked against an exact quantum mechanical treatment of the system, which is based on a highly efficient Chebyshev expansion technique of the time evolution operator., Comment: 32 pages, 8 figures, corrected typos and added references; version as published

In the tomography representation we propose a new approach, which describes the dynamics of quantum particles by the Kolmogorov equations for non-negative propagators. To solve the Kolmogorov equations we use a diffusive Markovian random processes described by the related nonlinear stochastic Langevin equations. As a result the dynamics of quantum particles is described by the proposed numerical scheme combining both Langevin dynamics and Monte Carlo methods. We test the developed approach by applying it to the wave packet dynamics in harmonic potentials and to particle tunneling through a barrier.

We study strong Coulomb correlations in dense two-dimensional electron–hole plasmas by means of direct path integral Monte Carlo simulations. In particular, the formation and dissociation of bound states, such as excitons, bi-excitons and many particle clusters, is analyzed and the density-temperature regions of their occurrence are identified. At high density, the Mott transition to the fully ionized state (electron–hole hexatic liquid) is detected. Particular attention is paid to the influence of the hole to electron mass ratio M on the properties of the plasma. For high enough values of M we observed the formation of Coulomb hole crystal-like structures.

First observations of the dust grain crystal formation in the plasma generated by the slowing-down proton beam have been described. The crystal being formed has a simple cubical lattice with the mean distances between particles for different gases (He, Ne, Ar, Kr, Xe) from 90 to 140 μm. For a calculation of parameters of plasma the model of kinetic processes was developed. Results of our simulation showed that the anisotropic dust particles interaction can be the main physical reason of the appearance of the crystal like structure.

Results are presented from experimental and theoretical investigations of the behavior of dust grains in a track plasma produced by a beam of accelerated protons. The dynamic ordered dust structures in a proton-beam-produced plasma are obtained for the first time. The processes leading to the formation of such structures are simulated numerically. The experimentally obtained dynamic vortex dust structures in a track plasma of a proton beam are explained theoretically, and the theoretical model developed to describe such a plasma is verified experimentally. Numerical investigations carried out by the method of Brownian dynamics made it possible to qualitatively explain the characteristic features of the formation of vortex dust structures.

The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the epxerimental progress in the field of warm dense matter. To explain the experimental data accurate theoretical models for high density plasmas are needed which crucially depend on the quality of the thermodynamic properties of the quantum degenerate correlated electrons. Recent fixed node path integral Monte Carlo (RPIMC) data are the most accurate for the UEG at finite temperature, but they become questionable at high degeneracy when the Brueckner parameter $r_s$ becomes smaller than $1$. Here we present new improved direct fermionic PIMC simulations that are exptected to be more accurate than RPIMC at high densities., arXiv admin note: text overlap with arXiv:cond-mat/0702049

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 included

Results for the dynamic structure factor of a one-component plasma are presented for the situations of strong coupling and weak degeneracy and strong degeneracy and weak coupling. Possibilities to obtain rigorous results when both, coupling and degeneracy are large are discussed., 4 pages, 2 eps figures, uses cpp2e style (included)

Ordered dusty structures formed of spherical monodisperse and polydisperse grains are obtained for the first time in a nuclear-track plasma produced by α-particles and fission fragments of 252Cf nuclei passing through neon or argon. A theoretical model of such a plasma is proposed. Monte Carlo computer simulations based on this model are carried out to explain the formation of such structures.

Using a novel path integral representation of the many-particle density operator, we calculate the pair distribution function of Fermi systems which are both strongly coupled and strongly degenerate . Numerical results are presented for a dense two-component electron–proton plasma at temperatures k B T >0.1 Ry.

A new numerical approach for the treatment of quantum dynamics and for the computation of average values of quantum operators and of time correlation functions in the Wigner representation of quantum statistical mechanics has been developed. For electrons in a disordered system of scatterers, new numerical results have been obtained for various average values of quantum operators, including the position and momentum dispersions, the average energy, the energy distribution function, and frequency-dependent tensors, such as the electron conductivity and the permittivity, which follow from the quantum Kubo formula.

The new numerical approach for investigation of strongly coupled systems including a subsystem of quantum particles and a subsystem of classical particles has been developed. The advanced approach combines and generalizes molecular dynamics and path integral Monte Carlo methods and allows investigating the dynamic and thermodynamic properties of degenerate particle systems. Numerical results for energy, pressure, pair correlation functions and frequency dependencies of tensor of electron conductivity.

An effective potential is proposed for the interaction between dust particles in a gas-discharge plasma which takes account of the following physical factors: the spatial dependence of the particle charges on the floating potential of the plasma, anisotropy of the interaction, resulting from focusing of the negatively charged particles of the drift ion current, and aspects of screening of the dust particles by plasma electrons and ions which interact strongly with them and recombine faster in their vicinity and on their surface. Monte Carlo calculations explain the formation of threadlike structures of dispersed particles, and also “transverse crystallization” of these “threads” in a stratified gas-discharge plasma.

The new numerical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation functions in the Wigner representation of quantum statistical mechanics has been developed. The time correlation functions have been presented in the form of the integral of the Weyl's symbol of considered operators and the Fourier transform of the product of matrix elements of the dynamic propagators. For electrons in disordered systems of scatterers the numerical results have been obtained for series of the average values of the quantum operators including position and momentum dispersions, average energy, energy distribution function as well as for the frequency dependencies of tensor of electron conductivity and permittivity according to quantum Kubo formula. Zero or very small value of static conductivity have been considered as the manifestation of Anderson localization of electrons in 1D case.

We have compared experimental measurements of ordered structures in a thermal plasma containing macroparticles of CeO2 at atmospheric pressure and a temperature around 1700 K with the results of numerical Monte Carlo calculations for the Yukawa model. We describe several distinctive features of the way the experiments were done, including how the ordered macroparticle structures were detected. We discuss a theoretical model of the behavior of an equilibrium system of charged macroparticles in a plasma and the effective interaction potential between them. Good agreement between the experimental and numerical results is noted, and possible reasons for the observed discrepancies are discussed.

Based on the quasiparticle model of the quark-gluon plasma (QGP), a color quantum path-integral Monte-Carlo (PIMC) method for calculation of thermodynamic properties and -- closely related to the latter -- a Wigner dynamics method for calculation of transport properties of the QGP are formulated. The QGP partition function is presented in the form of a color path integral with a new relativistic measure instead of the Gaussian one traditionally used in the Feynman-Wiener path integral. It is shown that the PIMC method is able to reproduce the lattice QCD equation of state at zero baryon chemical potential at realistic model parameters (i.e. quasiparticle masses and coupling constant) and also yields valuable insight into the internal structure of the QGP. Our results indicate that the QGP reveals quantum liquid-like (rather than gas-like) properties up to the highest considered temperature of 525 MeV. The pair distribution functions clearly reflect the existence of gluon-gluon bound states, i.e. glueballs, at temperatures just above the phase transition, while meson-like $q\bar{q}$ bound states are not found. The calculated self-diffusion coefficient agrees well with some estimates of the heavy-quark diffusion constant available from recent lattice data and also with an analysis of heavy-quark quenching in experiments on ultrarelativistic heavy ion collisions, however, appreciably exceeds other estimates. The lattice and heavy-quark-quenching results on the heavy-quark diffusion are still rather diverse. The obtained results for the shear viscosity are in the range of those deduced from an analysis of the experimental elliptic flow in ultrarelativistic heavy ions collisions, i.e. in terms the viscosity-to-entropy ratio, $1/4��< ��/S < 2.5/4��$, in the temperature range from 170 to 440 MeV., 23 pages, 17 figures, version accepted by Phys. Rev. C, technical problems with file fixed

The integral Wigner - Liouwille equation describing time evolution of the semi-relativistic quantum 1D harmonic oscillator have been exactly solved by combination of the Monte-Carlo procedure and molecular dynamics methods. The strong influence of the relativistic effects on the time evolution of the momentum, velocity and coordinate Wigner distribution functions and the average values of quantum operators have been studied. Unexpected 'protuberances' in time evolution of the distribution functions were observed. Relativistic proper time dilation for oscillator have been calculated., 10 pages, 26 figures. arXiv admin note: text overlap with arXiv:hep-th/0110114, arXiv:hep-ph/0501268, arXiv:math-ph/0702082 by other authors

Computational techniques allowing path-integral calculations are introduced and applied for a system of noninteracting electrons in a random potential of scatterers and an external electric field. The ensemble-averaged second (probability for electron travelling) and fourth moments of the Green function have been calculated. The numerical results have been obtained and compared with analytical results. The Monte Carlo results for 1D media have shown the existing singularities at the localization centres and forming exponential decay of the second moment at distances of about a wavelength. Unexpected sharp oscillations interrupting the exponential decay of the Green function moments have been obtained at distances of about tens of the average distances between scatterers from the centre localization. The effect of an external electric field on the behaviour of the second moment have also been investigated.

A new method for solving the Wigner-Liouville equation allowing a treatment of quantum dynamics has been developed. The method combines two widely known approaches: molecular dynamics and Monte Carlo. Numerical results have been obtained for one-, two- and three-dimensional potential wells of realistic type. The quantum dynamics method was tested by a comparison of the numerical results with analytical estimates for such values as the average position x¯(t), average momentum p¯(t), energy Ē(t), position and momentum dispersions, and Heisenberg inequality.

Thermodynamic properties of a strongly coupled quark–gluon plasma (QGP) of constituent quasiparticles are studied by a color path-integral Monte Carlo simulations (CPIMC). For our simulations we have presented QGP partition function in the form of color path integral with new relativistic measure instead of Gaussian one used in Feynman and Wiener path integrals. For integration over color variable we have also developed procedure of sampling color variables according to the group SU(3) Haar measure. It is shown that this method is able to reproduce the available quantum lattice chromodynamics (QCD) data.

Path integrals and a complex Monte Carlo method are used to describe wave propagation and localization in 1D, 2D, and 3D media with small-scale random and large-scale regular inhomogeneities. The probability of wave passage over distance\(|\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {r} - \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {r} '|\) averaged over an ensemble of scatterers is calculated. A comparison with analytical results is performed. Unexpected sharp peaks interrupting the exponential decay of the mean square absolute value of Green's function are detected numerically together with the possibility of wave delocalization in the presence of regular inhomogeneities.

A strongly coupled plasma of quark and gluon quasiparticles at temperatures from 1.1Tc to 3Tc 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 lattice results. Further, pair distribution functions and color correlation functions are computed indicating strong correlations and liquid-like behavior (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper studies two-dimensional electron-hole plasmas using the direct quantum path integral Monte Carlo method. Results are presented for 2D electron-hole plasmas in the wide region of temperature, density and electron to hole mass ratio. The calculations include region of appearance and decay of the bound state (excitons and biexcitons), Mott transition from neutral e-h plasma to metallic-like clusters, formation from clusters the hexatic-like liquid and then formation of the crystal-like lattice and at very low temperatures transition of this 'lattice' to antiferromagnetic structure.

In this paper the numerical procedure combining both molecular dynamics and Monte Carlo methods for solving the integral Wigner- Liouville equation has been developed and applications of this approach to the treatment of kinetic properties of quantum dense hydrogen plasma has been considered. To study the influence of the Coulomb interaction on kinetic properties of dense plasma the quantum dynamics in a canonical ensemble at finite temperature for both weakly and strongly coupled plasmas was simulated. The main quantities calculated are the temporal momentum-momentum correlation functions and their frequency-domain Fourier transforms.

In the standard formulation of quantum mechanics states of a system are described by wave functions or density operators . However quantum description of the system can be given in many other ways , for example, in Wigner-Moyal or Feynman formulations . All these representation are equivalent in the the sense of physical results, but the form of presentation of quantum mechanics is different as wave functions, Wigner-Liouville functions or other representations of density operators differ in essential way from each other. In this work we are dealing with Wigner and probability representation of quantum mechanics. The probability representations or tomography representation was recently proposed in terms of marginal distribution functions (MDF). MDF describing the quantum states are positive distribution functions connected with wave functions or density matrices by known integral transformation. Sign conservation of the of the MDF can be valuable in computer simulations to overcome the "sign problem". Important advantage of the probability representation is that the quantum transitions between quantum states are descried by non-negative probabilities. This work is devoted to the development of a new stochastic approaches to numerical solution of the evolution equations for Wigner-Liouviile (WL) and marginal distribution functions. To solve the WL equation we combine both molecular dynamics and Monte Carlo methods and compute traces of the dynamical operators. The results obtained for a system of electrons and random scatterers clearly demonstrate that the many-particle interaction between the electrons leads to an enhancement of the conductivity compared to the case of noninteracting electrons. To obtain evolution of MDF we developed new stochastic approach to solution of the generalized Langevin equation (GLE). GLE is derived from Kolmogorov equations for Green function of evolution equation for MDF. We discuss the basic relations and main ideas of this approach, compare obtained numerical results with results of independent finite-difference calculations for quantum oscillator and quantum particles crossing the finite well and tunneling through the Gaussian barrier.

We investigate structures of 2D quantum electron-hole (e-h) plasmas by the direct path integral Monte Carlo method (PIMC) in a wide range of temperature, density and hole-to-electron mass ratio. Our simulation includes a region of appearance and decay of the bound states (excitons and biexcitons), the Mott transition from the neutral e-h plasma to metallic-like clusters, formation from clusters the hexatic-like liquid and formation of the crystal-like lattice., Comment: Proceedings of the Strongly Coupled Coulomb Systems - 2008 conference, 4 pages, 2 figures, submitted to Journal of Physics A