The property of κ-deformed statistics for a relativistic gas in an electromagnetic field: κ parameter and κ-distribution

We investigate the physical property of the κ parameter and the κ-distribution in the κ-deformed statistics, based on Kaniadakis entropy, for a relativistic gas in an electromagnetic field. We derive two relations for the relativistic gas in the framework of κ-deformed statistics, which describe the physical situation represented by the relativistic κ-distribution function, provide a reasonable connection between the parameter κ  , the temperature four-gradient and the four-vector potential gradient, and thus present for the case κ≠0$\kappa \ne 0$ one clearly physical meaning. It is shown that such a physical situation is a meta-equilibrium state of the system, but has a new physical characteristic.     

Wave scattering by many small particles embedded in a medium

Theory of wave scattering by many small bodies is developed under various assumptions concerning the ratio , where a is the characteristic dimension of a small body and d is the distance between neighboring bodies d=O(aκ₁), 0<κ₁<1. On the boundary Sm of every small body an impedance-type condition is assumed on Sm, 1?m?M, ζm=hma−κ, 0<κ, hm are constants independent of a. The behavior of the field in the region in which M=M(a)?1 small particles are embedded is studied as a→0 and M(a)→∞. Formulas for the refraction coefficient of the limiting medium are derived under the assumptions: (a) κ₁=(2−κ)/3, 0<κ?1, and (b) κ₁=1/3, κ>1. A method for creating materials with a desired refraction coefficient is proposed and justified theoretically on the basis of the above results.     

Probability density,diagrammatic technique,and epsilon expansion in the theory of wave turbulence

We apply the methods of field theory to study the turbulent regimes of statistical systems. First we show how one can find their probability densities. For the case of the theory of wave turbulence with four-wave interaction we calculate them explicitly and study their properties. Using those densities we show how one can in principle calculate any correlation function in this theory by means of direct perturbative expansion in powers of the interaction. Then we give the general form of the corrections to the kinetic equation and develop an appropriate diagrammatic technique. This technique, while resembling that of ϕ⁴ theory, has many new distinctive features. The role of the ϵ = d − 4 parameter of ϕ⁴ theory is played here by the parameter κ = β + d − α − γ where β is the dimension of the interaction, d is the space dimension, α is the dimension of the energy spectrum and γ is the “classical” wave density dimension. If κ > 0 then the Kolmogorov index is exact, and if κ < 0 then we expect it to be modified by the interaction. For κ a small negative number, α < 1 and a special form of the interaction we compute this modification explicitly. We neglect the encountered IR divergencies with the intend to study them in a later publication.     

The chemical potential for the inhomogeneous electron liquid in terms of its kinetic and potential parts with special consideration of the surface potential step and BCS-BEC crossover

The chemical potential μ of a many-body system is valuable since it carries fingerprints of phase changes. Here, we summarize results for μ for a three-dimensional electron liquid in terms of average kinetic and potential energies per particle. The difference between μ and the energy per particle is found to be exactly the electrostatic potential step at the surface. We also present calculations for an integrable one-dimensional many-body system with delta function interactions, exhibiting a BCS-BEC crossover. It is shown that in the BCS regime the chemical potential can be expressed solely in terms of the ground-state energy per particle. A brief discussion is also included of the strong coupling BEC limit.     

The internal energy and thermodynamic behaviour of a boson gas below the Bose-Einstein temperature

We have examined the issue of the kinetic energy of particles in the ground state of an ideal boson gas. By assuming that the particles, on dropping into the ground state, retain the kinetic energy they possess at the Bose-Einstein temperature TB, we obtain new expressions for the pressure and internal energy of the gas below TB, that are free of the difficulties associated with the corresponding expressions in current theory. Furthermore, these new equations yield a value for the maximum density temperature in liquid ⁴He that is very close to the measured value.     

Spin-state transition, magnetic, electrical and thermal transport properties of the perovskite cobalt oxide Gd0.7Sr0.3CoO3

The magnetization, resistivity ρ, thermoelectric power (TEP) S, and thermal conductivity κ in perovskite cobalt oxide Gd_0.7Sr_0.3CoO₃ have been investigated systematically. Based on the temperature dependence of susceptibility χ_g(T) and Seebeck coefficient S(T), a combination of the intermediate-spin (IS) state for Co³⁺ and the low-spin (LS) state for Co⁴⁺ can be suggested. A metal-insulator transition (MIT) caused by the hopping of σ* electrons (localized or delocalized e_g electrons) from the IS Co³⁺ to the LS Co⁴⁺ is observed. Meanwhile, S(T) curve also displays an obvious phonon drag effect. In addition, based on the analysis of the temperature dependence of S(T) and ρ(T), the high-temperature small polaron conduction and the low-temperature variable-range-hopping conduction are suggested, respectively. As to thermal conduction κ(T), rather low κ values in the whole measured temperature range is attributed to unusually large local Jahn-Teller (JT) distortion of Co³⁺O₆ octahedra with IS state.     

Differential structure on κ-Minkowski spacetime realized as module of twisted Weyl algebra

The differential structure on the κ-Minkowski spacetime from Jordanian twist of Weyl algebra is constructed, and it is shown to be closed in 4-dimensions in contrast to the conventional formulation. Based on this differential structure, we have formulated a scalar field theory in this κ-Minkowski spacetime.     

Dynamical scaling and kinetic equations for heisenberg spin systems just below the critical temperature

We propose an approximate set of kinetic equations to describe the time evolution of spin correlation functions below T_c in a system with long-range interactions. In the ordered region, these equations lead to weakly damped spin waves, in exact agreement with the previous work of Vaks, Lakkin and Pikin. When T_c is approached, spin waves persist for q ? κ_, where κ_is the inverse correlation length but, for q ? κ_, these kinetic equations continuously transform into the non-Markoffian equation previously derived by one of the authors and De Leener above F_c. Moreover, dynamical scaling is microscopically justified in our model. Beyond the assumption of a large number of interacting neighbours, we also need the phenomenological hypothesis that, close to T_c, the equilibrium properties appearing in our kinetic equations can be described by their correct (nonclassical) critical indices.     

Kinetic theory of adsorption and desorption

In this paper we use stochastic methods to discuss adsorption and desorption. The paper derives generalized coefficients of sticking and accomodation depending on surface temperatureT _s and gas temperatureT _g and shows, that for additive Markov processes, these kinetic coefficients are identical. Furthermore, exact solutions of the kinetic equations for certain simple transition probabilitiesP(?, ?′) are found and an approximation method for more complicatedP(?, ?′) is given. The comparison of the theory with experimental results for noble gas-metal systems indicate a quadratic relationship between the first moment of the transition probabilityP(?, ?′) and the well depth of the physisorption system.     

Degenerate asymptotic perturbation theory

Asymptotic Rayleigh-Schrödinger perturbation theory for discrete eigenvalues is developed systematically in the general degenerate case. For this purpose we study the spectral properties ofm×m—matrix functionsA(κ) of a complex variable κ which have an asymptotic expansion εA _k κ ^k as τ→0. We show that asymptotic expansions for groups of eigenvalues and for the corresponding spectral projections ofA(κ) can be obtained from the set {A _κ} by analytic perturbation theory. Special attention is given to the case whereA(κ) is Borel-summable in some sector originating from κ=0 with opening angle >π. Here we prove that the asymptotic series describe individual eigenvalues and eigenprojections ofA(κ) which are shown to be holomorphic inS near κ=0 and Borel summable ifA _k ^* =A _k for allk. We then fit these results into the scheme of Rayleigh-Schrödinger perturbation theory and we give some examples of asymptotic estimates for Schrödinger operators.     

A spherically symmetric vacuum solution of the quadratic Poincaré gauge field theory of gravitation with newtonian and confinement potentials

We derive a stationary spherically symmetric vacuum solution in the framework of the Poincaré gauge field theory with a recently proposed quadratic lagrangian. We find a metric of the Schwarzschild-de Sitter type, both torsion and curvature are non vanishing, with torsion proportional to the mass and curvature proportional to the strong coupling constant κ. The metric exhibits two pieces, a newtonian potential describing the gravitational behavior of macroscopic matter, and a confining potential ～κr² presumably related to the strong-interaction properties of hadrons. To our knowledge this is a new feature of a classical solution of a Yang-Mills type gauge theory.     

From noncommutative κ-Minkowski to Minkowski space–time

We show that free κ-Minkowski space field theory, discussed in the context of κ-Poincaré algebra and Doubly Special Relativity is equivalent to a relativistically invariant free field theory on Minkowski space–time. The field theory we obtain has in spectrum a relativistic mode of arbitrary mass m and a Planck mass tachyon. We show that while the energy–momentum for the relativistic mode is essentially the standard one, it diverges for the tachyon, so that there are no asymptotic tachyonic states in the theory. It also follows that the dispersion relation is not modified, so that, in particular, in this theory the speed of light is energy-independent.     

Binding energies and modelling of nuclei in semiclassical simulations

We study the binding energies of spin–isospin saturated nuclei with nucleon number 8?A?100$8?A?100$ in semiclassical Monte Carlo many-body simulations. The model Hamiltonian consists of (i) nucleon kinetic energy, (ii) a nucleon–nucleon interaction potential, and (iii) an effective Pauli potential which depends on density. The basic ingredients of the nucleon–nucleon potential are a short-range repulsion, and a medium-range attraction. Our results demonstrate that one can always expect to obtain the empirical binding energies for a set of nuclei by introducing a proper density dependent Pauli potential in terms of a single variable, the nucleon number, A. The present work shows that in the suggested procedure there is a delicate counterbalance of kinetic and potential energetic contributions allowing a good reproduction of the experimental nuclear binding energies. This type of calculations may be of interest in further reproduction of other properties of nuclei such as radii and also exotic nuclei.     

Kinetic Monte Carlo simulations of electrodeposition: Crossover from continuous to instantaneous homogeneous nucleation within Avrami’s law

The influence of lateral adsorbate diffusion on the dynamics of the first-order phase transition in a two-dimensional Ising lattice gas with attractive nearest-neighbor interactions is investigated by means of kinetic Monte Carlo simulations. For example, electrochemical underpotential deposition proceeds by this mechanism. One major difference from adsorption in vacuum surface science is that under control of the electrode potential and in the absence of mass-transport limitations, local adsorption equilibrium is approximately established. We analyze our results using the theory of Kolmogorov, Johnson and Mehl, and Avrami (KJMA), which we extend to an exponentially decaying nucleation rate. Such a decay may occur due to a suppression of nucleation around existing clusters in the presence of lateral adsorbate diffusion. Correlation functions prove the existence of such exclusion zones. By comparison with microscopic results for the nucleation rate I and the interface velocity of the growing clusters v, we can show that the KJMA theory yields the correct order of magnitude for Iv². This is true even though the spatial correlations mediated by diffusion are neglected. The decaying nucleation rate causes a gradual crossover from continuous to instantaneous nucleation, which is complete when the decay of the nucleation rate is very fast on the time scale of the phase transformation. Hence, instantaneous nucleation can be homogeneous, producing negative minima in the two-point correlation functions. We also present in this paper an n-fold way Monte Carlo algorithm for a square lattice gas with adsorption/desorption and lateral diffusion.     

The Ginzburg–Landau theory and the surface energy of a colour superconductor

We apply the Ginzburg–Landau theory to the colour superconducting phase of a lump of dense quark matter. We calculate the surface energy of a domain wall separating the normal phase from the super phase with the bulk equilibrium maintained by a critical external magnetic field. Because of the symmetry of the problem, we are able to simplify the Ginzburg–Landau equations and express them in terms of two components of the di-quark condensate and one component of the gauge potential. The equations also contain two dimensionless parameters: the Ginzburg–Landau parameter κ and ρ. The main result of this paper is a set of inequalities obeyed by the critical value of the Ginzburg–Landau parameter—the value of κ for which the surface energy changes sign—and its derivative with respect to ρ. In addition we prove a number of inequalities of the functional dependence of the surface energy on the parameters of the problem and obtain a numerical solution of the Ginzburg–Landau equations. Finally a criterion for the types of colour superconductivity (type I or type II) is established in the weak coupling approximation.     

Hydrodynamic Limit of a B.G.K. Like Model on Domains with Boundaries and Analysis of Kinetic Boundary Conditions for Scalar Multidimensional Conservation Laws

In this paper we study the hydrodynamic limit of a B.G.K. like kinetic model on domains with boundaries via BV _loc theory. We obtain as a consequence existence results for scalar multidimensional conservation laws with kinetic boundary conditions. We require that the initial and boundary data satisfy the optimal assumptions that they all belong to L ¹∩L ^∞ with the additional regularity assumptions that the initial data are in BV _loc . We also extend our hydrodynamic limit analysis to the case of a generalized kinetic model to account for forces effects and we obtain as a consequence the existence theory for conservation laws with source terms and kinetic boundary conditions.     

On κ-deformation and triangular quasibialgebra structure

We show that, up to terms of order κ⁻⁵${\kappa }^{\mathrm{-5}}$, the κ-deformed Poincaré algebra can be endowed with a triangular quasibialgebra structure. The universal R matrix and coassociator are given explicitly to the first few orders. In the context of κ-deformed quantum field theory, we argue that this structure, assuming it exists to all orders, ensures that states of any number of identical particles, in any representation, can be defined in a κ-covariant fashion.