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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

A recently developed fermionic path integral Monte Carlo approach [Filinov et al., Phys. Rev. E 102, 033203 (2020) and Filinov et al., J. Phys. A 55, 035001 (2021)] has been applied for the estimation of the density–temperature range of exchange–correlation exciton existence in a strongly coupled degenerate uniform electron gas. The approach allows us to reduce the “fermionic sign problem” taking into account the interference effects of the Coulomb and exchange interaction of electrons in the basic Monte Carlo cell and its periodic images. Our results for radial distribution functions demonstrate the formation and decay of a short-range quantum ordering of electrons associated with exchange–correlation excitons in the literature. Such excitons have never been observed earlier in standard path integral Monte Carlo simulations.

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.

The charging of Al2O3 macroparticles with dimensions ranging from 20 to 40 μm in a gas flow passing through a multielectrode corona discharge is investigated. The corona discharge is produced by a system of wire electrodes arranged across the gas flow. The particle charge and mass are measured using a linear electrodynamic trap. For a corona voltage of 18 kV, the average charge-to-mass ratio is found to be 1.69 × 1013e/g for particles charged in the positive corona and 1.35 × 1013e/g for particles charged in the negative corona.

A method against dust pollution of dielectric surfaces has been proposed. The dust removal is achieved applying alternating electric fields of special geometry created by the linear electrodynamic Paul traps, which polarize dust particles on the surface of the dielectric and draw them into the interelectrode space of the trap. The captured dust can be moved without contact with the solar panel surface toward the electrodes ends in a special container by an additional constant electric field. The feasibility of the approach was demonstrated by a series of experiments on the removal of aluminium oxide and sand particles of various sizes from a glass surface and solar panels. The cleaning rate for 70 90 μm particles uniformly scattered on the glass substrate inclined at 20∘ was 92%. The capture of a single particle was analyzed using numerical simulations and the conditions necessary for its capturing and levitating were determined.

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 interference and exchange statistical effects can affect the momentum distribution functions making them non-Maxwellian. Such effects may be important in studies of kinetic properties of matter at low temperatures and under extreme conditions. In this work we have generalized the path integral representation for Wigner function to strongly coupled three-dimensional quantum system of particles with Boltzmann and Fermi statistics. In suggested approach the explicit expression for Wigner function was obtained in harmonic approximation and Monte Carlo method allowing numerical calculation of Wigner function, distribution functions and average quantum values has been developed. As alternative more accurate single-momentum approach and related Monte Carlo method have been developed to calculation of the distribution functions of degenerate system of interacting fermions. It allows partially overcoming the well-known sign problem for degenerate Fermi systems.

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)

The possibility of charged particles trapped by the linear quadrupole Paul trap to form an ensemble with strong Coulomb interaction at atmospheric pressure has been experimentally shown. The ordered structure could confine particles of different sizes and charges. Stable clouds of thousands of oxide aluminum particles with sizes of 0.5÷65 microns were observed in the linear trap with electrodes placed 30 mm apart. (© 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.

The behavior of the charged dust particles in the linear Paul trap was simulated by Brownian dynamics for reasonable choice of the particle parameters and trap electrode voltages. Regions of these parameters needed for particle confinement at normal atmosphere conditions (pressure and temperatures) have been obtained. An influence of air viscosity, particle masses and charges, frequency and alternating voltage on regions of confinement were investigated. Obtained regions of the particle confinement agree with our experimental results for linear Paul trap. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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)

A model of a corona discharge in a nuclear excited dust plasma at the pressures of 1–100 atm is proposed. The distributions of the electric field and current-voltage characteristics of a corona discharge in a nuclear-excited dust plasma are found for a particular cylindrical geometry case at different methods of corona-producing electrode positioning. The conditions for the existence of a stationary corona discharge are obtained. A mathematical model describing the behavior of dust particles in a nuclear plasma that allows taking into account the key physical processes occurring in a nuclear-excited dust plasma is considered. The analyzed plasma properties are as follows: (1) shielding of the Coulomb forces of the interaction between dust particles, (2) the energy exchange and the stochastic character of the dust particle interaction with a buffer gas and ambient plasma, and (3) strong spatial inhomogeneity of the nuclear-excited plasma. The use of a corona discharge in a nuclear-excited plasma will make it possible to ensure stability of plasma-dust structures and more efficient conversion of the nuclear energy into laser radiation.

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)

Noble metals that are deposited on a polymer surface exhibit surface diffusion and diffusion into the bulk. At the same time the metal atoms tend to form clusters because their cohesive energy is about two orders of magnitude higher than the cohesive energy of polymers. To selfconsistently simulate these coupled processes, we present in this paper a Kinetic Monte Carlo approach. Using a simple model with diffusion coefficients taken as input parameters allows us to perform a systematic study of the behavior of a large ensemble of metal atoms on a polymer surface eventually leading to polymer nanocomposites. Special emphasis is placed on the cluster growth, cluster size distribution and the penetration of clusters into the substrate. We also study the influence of surface defects and analyze how the properties of the resulting material can be controlled by variation of the deposition rate (© 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 paper presents the simulation results of micro- and nanoparticle capturing in an air flows by linear Paul traps in assumption that particles gain their charges in corona discharge, its electric field strength is restricted by Paschen equation and spherical shape of particles.

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.

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

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.