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

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

On the Static Dielectric Permittivity for Coulomb System in the Long Wavelength Limit

On the basis of the exact relations the general formula for the static dielectric permittivity for Coulomb system is found in the region of small wave vectors. The obtained formula describes the dielectric function of the Coulomb system in both limits: in the "metallic" state and in the "dielectric" one. On this basis the determinations of the "apparent" dielectric and the "apparent" radius of screening are introduced. In the random phase approximation (RPA) the exact relations for the function dielectric function of the electron gas in the long-wavelength region of the wave vectors are found for an arbitrary degeneration of the particles.Comment: 5 pages, no figure

Angular Schmidt Modes in Spontaneous Parametric Down-Conversion

We report a proof-of-principle experiment demonstrating that appropriately chosen set of Hermite-Gaussian modes constitutes a Schmidt decomposition for transverse momentum states of biphotons generated in the process of spontaneous parametric down conversion. We experimentally realize projective measurements in Schmidt basis and observe correlations between appropriate pairs of modes. We perform tomographical state reconstruction in the Schmidt basis, by direct measurement of single-photon density matrix eigenvalues.Comment: 5 pages, 4 figure

Competition of multiband superconducting and magnetic order in ErNi2B2C observed by Andreev reflection

Point contacts (PC) Andreev reflection dV/dI spectra for the antiferromagnetic (T_N =6K) superconductor (Tc=11K) ErNi2B2C have been measured for the two main crystallographic directions. Observed retention of the Andreev reflection minima in dV/dI up to Tc directly points to unusual superconducting order parameter (OP) vanishing at Tc. Temperature dependence of OP was obtained from dV/dI using recent theory of Andreev reflection including pair-breaking effect. For the first time existence of a two superconducting OPs in ErNi2B2C is shown. A distinct decrease of both OPs as temperature is lowered below T_N is observed.Comment: 5 pages, 5 figs, to be published in Europhys. Let

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

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

Observation of anisotropic effect of antiferromagnetic ordering on the superconducting gap in ErNi2B2C

The point-contact (PC) spectra of the Andreev reflection dV/dI curves of the superconducting rare-earth nickel borocarbide ErNi2B2C (Tc=11 K) have been analyzed in the "one-gap" and "two-gap" approximations using the generalized Blonder-Tinkham-Klapwijk (GBTK) model and the Beloborod'ko (BB) model allowing for the pair-breaking effect of magnetic impurities. Experimental and calculated curves have been compared not only in shape, but in magnitude as well, which provide more reliable data for determining the temperature dependence of the energy gap (or superconducting order parameter) \Delta(T). The anisotropic effect of antiferromagnetic ordering at T_N =6 K on the superconducting gap/order parameter has been determined: as the temperature is lowered, \Delta(T) decreases by 25% in the c-direction and only by 4% in the ab-plane. It is found that the pair-breaking parameter increases in the vicinity of the magnetic transitions, the increase being more pronounced in the c-direction. The efficiency of the models was tested for providing \Delta(T) data for ErNi2B2C from Andreev reflection spectra.Comment: 16 two column pages, 20 figs., will be published in Fiz. Nizk. Temp. N10, 2010; V2: added - "Acknowledgement" & "Note added in proof