Kramers-Kronig Relations For The Dielectric Function And The Static Conductivity Of Coulomb Systems

The mutual influence of singularities of the dielectric permittivity e(q,w) in a Coulomb system in two limiting cases w tends to zero, q tends to zero, and opposite q tends to zero, w tends to zero is established. It is shown that the dielectric permittivity e(q,w) satisfies the Kramers-Kronig relations, which possesses the singularity due to a finite value of the static conductivity. This singularity is associated with the long "tails" of the time correlation functions.Comment: 9 pages, 0 figure

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

Identity of electrons and ionization equilibrium

It is perhaps appropriate that, in a year marking the 90th anniversary of Meghnad Saha seminal paper (1920), new developments should call fresh attention to the problem of ionization equilibrium in gases. Ionization equilibrium is considered in the simplest "physical" model for an electronic subsystem of matter in a rarefied state, consisting of one localized electronic state in each nucleus and delocalized electronic states considered as free ones. It is shown that, despite the qualitative agreement, there is a significant quantitative difference from the results of applying the Saha formula to the degree of ionization. This is caused by the fact that the Saha formula corresponds to the "chemical" model of matter.Comment: 9 pages, 2 figure

On anomalous diffusion in a plasma in velocity space

The problem of anomalous diffusion in momentum space is considered for plasma-like systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in momentum space. The generalized Fokker-Planck equation for description of diffusion (in momentum space) of particles (ions, grains etc.) in a stochastic system of light particles (electrons, or electrons and ions, respectively) is applied to the evolution of the momentum particle distribution in a plasma. In a plasma the developed approach is also applicable to the diffusion of particles with an arbitrary mass relation, due to the small characteristic momentum transfer. The cases of an exponentially decreasing in momentum space (including the Boltzmann-like) kernel in the PT-function, as well as the more general kernels, which create the anomalous diffusion in velocity space due to the long tail in the PT-function, are considered. Effective friction and diffusion coefficients for plasma-like systems are found.Comment: 18 pages, no figure

True Dielectric and Ideal Conductor in Theory of the Dielectric Function for Coulomb System

On the basis of the exact relations the general formula for the static dielectric permittivity e(q,0) for Coulomb system is found in the region of small wave vectors q. The obtained formuladescribes the dielectric function e(q,0) of the Coulomb system in both states in the "metallic" state and in the "dielectric" one. The parameter which determines possible states of the Coulomb system - from the "true" dielectric till the "ideal" conductor is found. The exact relation for the pair correlation function for two-component system of electrons and nuclei g_ei(r) is found for the arbitrary thermodynamic parameters.Comment: 5 pages, no figure

Exact limiting relation between the structure factors in neutron and x-ray scattering

The ratio of the static matter structure factor measured in experiments on coherent X-ray scattering to the static structure factor measured in experiments on neutron scattering is considered. It is shown theoretically that this ratio in the long-wavelength limit is equal to the nucleus charge at arbitrary thermodynamic parameters of a pure substance (the system of nuclei and electrons, where interaction between particles is pure Coulomb) in a disordered equilibrium state. This result is the exact relation of the quantum statistical mechanics. The experimental verification of this relation can be done in the long wavelength X-ray and neutron experiments.Comment: 7 pages, no figure

Exploring Pompeii: discovering hospitality through research synergy

Hospitality research continues to broaden through an ever-increasing dialogue and alignment with a greater number of academic disciplines. This paper demonstrates how an enhanced understanding of hospitality can be achieved through synergy between archaeology, the classics and sociology. It focuses on classical Roman life, in particular Pompeii, to illustrate the potential for research synergy and collaboration, to advance the debate on hospitality research and to encourage divergence in research approaches. It demonstrates evidence of commercial hospitality activities through the excavation hotels, bars and taverns, restaurants and fast food sites. The paper also provides an example of the benefits to be gained from multidisciplinary analysis of hospitality and tourism

Analysis of linear and nonlinear conductivity of plasma-like systems on the basis of the Fokker-Planck equation

The problems of high linear conductivity in an electric field, as well as nonlinear conductivity, are considered for plasma-like systems. First, we recall several observations of nonlinear fast charge transport in dusty plasma, molecular chains, lattices, conducting polymers and semiconductor layers. Exploring the role of noise we introduce the generalized Fokker-Planck equation. Second, one-dimensional models are considered on the basis of the Fokker-Planck equation with active and passive velocity-dependent friction including an external electrical field. On this basis it is possible to find the linear and nonlinear conductivities for electrons and other charged particles in a homogeneous external field. It is shown that the velocity dependence of the friction coefficient can lead to an essential increase of the electron average velocity and the corresponding conductivity in comparison with the usual model of constant friction, which is described by the Drude-type conductivity. Applications including novel forms of controlled charge transfer and non-Ohmic conductance are discussed.Comment: 14 pages with 6 figure