Energy of vacancy formation in the continuum matter model

The quantum energy spectrum of the oscillating spherical void in solids is calculated within the continuum matter model. It is suggested that the ground state of the oscillating void corresponds to the vacancy in real crystals. The dependence of the vacancy formation energy on the shear modulus, density, pressure and surface tension is determined. The obtained results are used to estimate properties of vacancies in solid Ar. A possibility to use the obtained results to estimate the properties of vacancies in liquid melts is discussed

Velocity-Dependent Friction and Diffusion for Grains in Neutral Gases, Dusty Plasmas and Active Systems

A self-consistent and universal description of friction and diffusion for Brownian particles (grains) in different systems, as a gas with Boltzmann collisions, dusty plasma with ion absorption by grains, and for active particles (e.g., cells in biological systems) is suggested on the basis of the appropriate Fokker-Planck equation. Restrictions for application of the Fokker-Planck equation to the problem of velocity-dependent friction and diffusion coefficients are found. General description for this coefficient is formulated on the basis of master equation. Relation of the diffusion coefficient in the coordinate and velocity spaces is found for active (capable to transfer momentum to the ambient media) and passive particles in the framework of the Fokker-Planck equation. The problem of anomalous space diffusion is formulated on the basis of the appropriate probability transition (PT) function. The method of partial differentiation is avoided to construct the correct probability distributions for arbitrary distances, what is important for applications to different stochastic problems. Generale equation for time-dependent PT function is formulated and discussed. Generalized friction in the velocity space is determined and applied to describe the friction force itself as well as the drag force in the case of a non-zero driven ion velocity in plasmas. The negative friction due to ion scattering on grains exists and can be realized for the appropriate experimental conditions.Comment: 21 page

Fokker-Planck Equation for Boltzmann-type and Active Particles: transfer probability approach

Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction and diffusion for Brownian particles. Renormalization of the friction coefficient is shown to occur for two dimensional (2-D) and three dimensional (3-D) cases, due to the tensorial character of diffusion. The specific forms of PT are calculated for the Boltzmann-type of collisions and for the absorption-type of collisions (the later are typical for dusty plasmas and some other systems). Validity of the Einstein's relation for the Boltzmann-type collisions is analyzed for the velocity-dependent friction and diffusion coefficients. For the Boltzmann-type collisions in the region of very high grain velocity as well as it is always for non-Boltzmann collisions, such as, e.g., absorption collisions, the Einstein relation is violated, although some other relations (determined by the structure of PT) can exist. The generalized friction force is investigated in dusty plasma in the framework of the PT approach. The relation between this force, negative collecting friction force and scattering and collecting drag forces is established.+AFwAXA- The concept of probability transition is used to describe motion of active particles in an ambient medium. On basis of the physical arguments the PT for a simple model of the active particle is constructed and the coefficients of the relevant Fokker-Planck equation are found. The stationary solution of this equation is typical for the simplest self-organized molecular machines.+AFwAXA- PACS number(s): 52.27.Lw, 52.20.Hv, 52.25.Fi, 82.70.-yComment: 18 page

Approximate k-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number {\kappa}. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C_{s} from the valence energy spectrum of particle and also for pseudospin symmetry constant C_{ps} from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter {\alpha}. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when {\alpha} becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.Comment: 21 pages, 6 figure

Shear viscosity of the Quark-Gluon Plasma from a virial expansion

We calculate the shear viscosity $\eta$ in the quark-gluon plasma (QGP) phase within a virial expansion approach with particular interest in the ratio of $\eta$ to the entropy density $s$, i.e. $\eta/s$. The virial expansion approach allows us to include the interactions between the partons in the deconfined phase and to evaluate the corrections to a single-particle partition function. In the latter approach we start with an effective interaction with parameters fixed to reproduce thermodynamical quantities of QCD such as energy and/or entropy density. We also directly extract the effective coupling \ga_{\rm V} for the determination of $\eta$. Our numerical results give a ratio $\eta/s\approx 0.097$ at the critical temperature $T_{\rm c}$, which is very close to the theoretical bound of $1/(4\pi)$. Furthermore, for temperatures $T\leq 1.8 T_{\rm c}$ the ratio $\eta/s$ is in the range of the present experimental estimates $0.1-0.3$ at RHIC. When combining our results for $\eta/s$ in the deconfined phase with those from chiral perturbation theory or the resonance gas model in the confined phase we observe a pronounced minimum of $\eta/s$ close to the critical temperature $T_{\rm c}$.Comment: Published in Eur. Phys. J. C, 7 pages, 2 figures, 3 tabl

Direct evaluation of the physical characteristics of Yukawa fluids based on a simple approximation for the radial distribution function

© 2020 The Authors We propose a simple analytical approximation for the radial distribution function (RDF) in a single-component Yukawa fluid. The proposed RDF depends on the two input parameters – the non-ideality parameter Γ and the structure (screening) parameter κ, which determine the thermodynamic state of Yukawa systems. We demonstrate that various physical properties can be directly calculated using the proposed RDF. In particular, the internal energy and pressure, the excess entropy in the pair approximation, and the dispersion relation of longitudinal acoustic-like collective excitations are calculated. These theoretical results are compared with the results from molecular dynamics simulations and good overall agreement is observed in the investigated regime of screening and coupling parameters