Kramers–Kronig Relations in Representation of Modulation Polarimetry by an Example of the Transmission Spectra of GaAs Crystal

The increments of the real and imaginary components of the complex refractive index ΔN = Δn–iΔk of a lightly doped GaAs crystal with a donor concentration of ~10¹⁶ cm^–3 have been measured using modulation polarimetry. It is shown that, within this representation, the birefringence and dichroism spectra (Δn(ω) and Δk(ω), respectively) obtained in the transparency window of a sample subjected to probe strain are derivatives of the corresponding functions: Δn(ω) ≈ dn/dω and Δk(ω) ≈ dk/dω. The experimental characteristics and primary dependences n(ω) and k(ω) derived from them by graphical integration are in agreement with the results of other researchers and measurements carried out by independent methods. The results obtained are compared (taking into account the integral (Kramers–Kronig) relations) with the resonance parameters: amplitude and phase in the Drude–Lorenz model. Agreement between the experimental characteristics and theoretical model predictions can be obtained by choosing an appropriate value of resonance damping parameter.     

On the energy transport velocity in a dissipative medium

An exact definition of the group velocity v _g is proposed for a wave process with arbitrary dispersion relation ω = ω′(k) + iω″(k). For the monochromatic approximation, a limit expression v _g (k) is obtained. A condition under which v _g (k) takes the form of the Kuzelev–Rukhadze expression [1] dω′(k)/dk is found. In the general case, it appears that v _g (k) is defined not only by the dispersion relation ω(k), but also by other elements of the initial problem. As applied to the dissipative medium, it is shown that v _g (k) defines the field energy transfer velocity, and this velocity does not exceed thee light speed in vacuum. An expression for the energy transfer velocity is also obtained for the case where the dispersion relation is given in the form k = k′(ω) + ik″(ω) which corresponds to the boundary problem.     

Propagation of electromagnetic waves in hot magnetoactive plasma

The paper derives the general form of the tensor of dielectric permittivity? _ij(ω,k), Eq. (15), of non-relativistic hot magnetoactive collisionless plasma taking into consideration the influence of spatial dispersion. The general form of the tensor? _ij(ω,k) is used to express the tensorε _ij(ω,k) in the region of weak and strong spatial dispersion and in some special cases. A general dispersion equation (30) is derived and an analysis is made of the waves propagating in hot magnetoactive plasma. The expressions derived are used to investigate the damping of a right-handed circularly polarized wave propagating in hot magnetoactive plasma in the direction of the magnetic field.     

Diamagnetism and the dispersion of the magnetic permeability

It is well known that the usual Kramers–Kronig relations for the relative permeability function μ(ω) are not compatible with diamagnetism (μ(0) < 1) and a positive imaginary part (Im μ(ω) > 0 for ω > 0). We demonstrate that a certain physical meaning can be attributed to μ for all frequencies, and that in the presence of spatial dispersion, μ does not necessarily tend to 1 for high frequencies ω and fixed wavenumber k. Taking the asymptotic behavior into account, diamagnetism can be compatible with Kramers–Kronig relations even if the imaginary part of the permeability is positive. We provide several examples of diamagnetic media and metamaterials for which μ(ω, k) ?  1 as ω →∞.     

Zero-sound branches in asymmetric nuclear matter

A polarization operator constructed in the random phase approximation is used to obtain zero-sound excitations in isospin asymmetric nuclear matter (ANM). Two families of the complex solutions ω_sτ(k),τ= p,n are presented. The imaginary part of the solutions corresponds to the damping of the collective mode due to its overlapping with the particle-hole modes and the subsequent emission of a proton (ω_sp(k)) or a neutron (ω_sn(k)). The dependence of the solutions on the asymmetry parameter is studied.     

Branches of zero sound excitations in asymmetric nuclear matter: The dependence on density

Results from calculating zero sound excitations in isospin asymmetric nuclear matter are presented. A polarization operator constructed in the random phase approximations is used in the calculations. Three branches of the complex solutions ω_sτ(k), τ = p,n,np are presented. The type of branch depends on that of the considered branch damping. An imaginary part of the solution corresponds to the damping of collective excitations due to mixing with the background of noninteracting (1) proton particle–hole pairs (ω _sp (k)), (2) neutron particle–hole pairs (ω _sn (k)), and (3) both proton and neutron particle–hole pairs (ω _snp (k)). The behavior of the solutions upon variations in density depends on the value of the asymmetry parameter.     

Magnetic impurities in a two-dimensional superfluid Fermi gas with spin-orbit coupling

We study magnetic impurities in a two dimensional superfluid Fermi gas with thespin-orbit coupling and find that the spin-orbit coupling makes some dramatic impacts onthe effects of magnetic impurities. For the single impurity problem, we find that thenumber of bound states localized around the magnetic impurity is doubled. For the finiteconcentration n of impurities, we find that the energy gap is reduced andthe density of states in the gapless region is greatly modified; there exists a gaplesssuperfluid and N(ω) ∝ ω in the smallω limit.     

Influence of the dimension of a polycrystalline film and the optical anisotropy of crystallites on the effective dielectric constant of the film

The dimension D of a polycrystalline film and the optical anisotropy m = ε_z/ε_x of uniaxial crystallites with the principal components ε_x = ε_y and ε_z of the tensor of the dielectric constant have been shown to produce a strong influence on the effective dielectric constant ε_D^* and the effective refractive index n_D^* = (ε_D^*)^1/2 of the film in the optical transparency region, as well as on the boundaries of the intervals B_Dl ≤ ε_D^* ≤ B_Du. The intervals Δ₂(m) = B_2l–B_2u and Δ₃(m) = B_3l–B_3u are separated by a gap for m in the range 1 < m < 2, whereas the theoretical dependence ε₂^*(m) is separated by a gap from the interval Δ₃(m) for m in the range 1 < m < 4. This is confirmed by a comparison of the experimental (n_oP) and theoretical (n_D^*) ordinary refractive indices for uniaxial polycrystalline films of the conjugated polymer poly(p-phenylene vinylene) (PPV) with uniaxial crystallites and appropriate values of m. In the visible transparency region of the PPV films with a change in m(λ) in the range 2 < m(λ) < 3 due to the dependence of the components ε_x,z(λ) on the light wavelength λ, the refractive indices n_oP²(λ) = ε_oP(λ) are consistent with the theoretical values of ε₂^*(λ) and lie outside the interval Δ₃(m). For m(λ) > 3 near the electronic absorption band of the crystallites, the values of ε_oP(λ) lie in the region of the overlap of the intervals Δ₂(m) and Δ₃(m). The boundaries mc of the range 1 < m < m_c are determined, for which the interval Δ₂(m) is separated by a gap from the dependences ε₃^*(m) corresponding to the effective medium theory with spherical crystallites and hierarchical models of a polycrystal, as well as from the proposed new dependence ε₃^*(m).     

Dielectric relaxations,magnetodielectric and magnetoelectric interactions in Bi0.6La0.4MnO3 ceramics

Complex permittivity ε*/ε₀ = ε′/ε₀–iε″/ε₀ of the bismuth–lanthanum manganite Bi_0.6La_0.4MnO₃ ceramics has been measured in the temperature range of 10–220 K at frequencies f = 20–10⁶ Hz and magnetic inductions B = 0–0.846 T. At a temperature of 80 K, the spectra ε′/ε₀(t) and ε″/ε₀(t) demonstrate the dielectric relaxation that is a superposition of contributions of several relaxation processes, each of which is dominant in its frequency range: I (f < 10³ Hz, II (10³ < f < 10⁵ Hz), and III (10⁵ < f < 10⁶ Hz). In the range of 10–120 K, anomalous behavior of ε′/ε₀(T) and ε″/ε₀(T) is observed near the temperature of the transition from the paramagnetic to ferromagnetic phase and is due to the Anderson localization of charge carrier on a spin disorder.     

Low-Temperature Transport Properties of Lanthanum Hexaboride La<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>Ce<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>B<Subscript>6</Subscript> Single Crystals

Resistivity (ρ), thermal conductivity (k) and Seebeck coefficient (S) of La_1–xCe_xB₆ single crystals with various concentrations of cerium Ce ions was measured in a wide temperature range 3?300 K. The obtained data were analyzed in the framework of the Coqblin–Shrieffer model. The contributions of scattering of carriers on magnetic ions Ce for all transport parameters ρ(T), k(T), S(T) are revealed. Strong dependence of the magnetic scattering on concentration of the cerium ions are identified. The anomalous behavior of the transport parameters ρ(T), k(T), S(T) in the region near 30 K is attributed to the Δ ~ 30 K splitting of Г₈ level.     

Crystal structure and magnetic susceptibility of (CuInSe<Subscript>2</Subscript>)<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>(2MnSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

The crystal structure of samples in the (CuInSe₂)_{1 ? x} (2MnSe) _x system at room temperature and their magnetic susceptibility in the temperature range 77–1000 K are investigated. It is established that compositions with concentrations 0≤ x ≤ 0.2 form solid solutions with a tetragonal structure, space group I \(\bar 4\)2d (122). The specific magnetic susceptibility χ of samples with 0.1 ≤ x ≤ 0.4 at 77 K lies in the range 9 × 10^?4?1.6 × 10^t-3cm³/g. The temperature dependence of the inverse magnetic susceptibility of the sample with x = 0.4 suggests the presence of a component with antiferromagnetic ordering and a reliably measured Néel temperature that is characteristic of MnSe. The dependences χ = f(T) of the compositions with x = 0.1, 0.2, 0.3, and 0.4 indicate the occurrence of magnetic phase transitions with a change in the spin state.     

Aussagen der Theorie von Kraichnan für die isotrope hydromagnetische Turbulenz

The theory ofKraichnan is applied to quasi-stationary isotropic hydromagnetic turbulence. The average infinitesimal-impulse-response functionsg(k, τ), g _m (k, τ) and the time-correlationsr(k, τ), r _m (k, τ) are evaluated by the non-local direct-interaction approximation within the inertial range. For the range of ohmic but no viscous dissipation it is found that the magnetic energy spectrumE _m (k) obeys aE(k)k ^?2-law in accordance with results ofGolitsyn andMoffatt.     

Transient bi-fractional diffusion: space-time coupling inducing the coexistence of two fractional diffusions

Anomalous diffusion is researched within the framework of the coupled continuous time random walk model, in which the space-time coupling is considered through the correlated function g(t) ~ t ^γ , 0 ≤ γ< 2, and the probability density function ω(t) of a particle’s transition time t follows a power law for large t: ω(t) ~ t ^{? (1 + α)},1 <α< 2. The bi-fractional generalized master equation is derived analytically which can be applied to describe the transient bi-fractional diffusion phenomenon which is induced by the space-time coupling and the asymptotic behavior of ω(t). Numerical results show that for the transient bi-fractional diffusion, there is a transition from one fractional diffusion to another one in the diffusive process.     

Über eine Näherung für Gitterelektronen in äußeren Feldern

The Hamilton operator of an electron in a periodic lattice potential under influence of external electric and magnetic fields with potentialsV(r) andA(r) resp. is often replaced by an approximate operatorW ⁰ (?i?+A(r))+V(r) for one single energy bandW ⁰(k) which means a renormalization of the kinetic energy by the lattice. The validity of this replacement is examined and the magnitude of its error is roughly estimated. Neglecting other bands one obtains an error term proportional to the derivative of the electric field strengthF, if one takes a suitable position of the “raster” of the replacement operator, and to the square of the magnetic field strengthB resp. The decoupling from the other energy bands leads to error terms proportionalF ² andB ² resp. which however in the general case increase rapidly in the vicinity of overlapping energy bands.     

Waves in a superlattice with arbitrary interlayer boundary thickness

The transmittance D(ω), reflectance R(ω), and dispersion ω(k) are investigated for waves of various nature propagating through a one-dimensional superlattice (multilayer structure) with arbitrary thickness of the interlayer boundary. The dependences of the band gap widths δω_m and their positions in the wave spectrum of the superlattice on the interlayer boundary thickness d and the band number m are calculated. Calculations are performed in terms of the modified coupled-mode theory (MCMT) using the frequency dependence of R(ω), as well as in the framework of perturbation theory using the function ω (k), which made it possible to estimate the accuracy of the MCMT method; the MCMT method is found to have a high accuracy in calculating the band gap widths and a much lower accuracy in determining the gap positions. It is shown that the m dependence of δω _m for electromagnetic (or elastic) waves is different from that for spin waves. Furthermore, the widths of the band gaps with m=1 and 2 are practically independent of d, whereas the widths of all gaps for m>2 depend strongly on d. Experimental measurements of these dependences allow one to determine the superlattice interface thicknesses by using spectral methods.     

Dielectric relaxation and ac conductivity of sodium tungsten phosphate glasses

Studies of dielectric relaxation and ac conductivity have been made on three samples of sodium tungsten phosphate glasses over a temperature range of 77–420 K. Complex relative permitivity data have been analyzed using dielectric modulus approach. Conductivity relaxation frequency increases with the increase of temperature. Activation energy for conductivity relaxation has also been evaluated. Measured ac conductivity (σ_m(ω)) has been found to be higher than σ_dc at low temperatures whereas at high temperature σ_m(ω) becomes equal to σ_dc at all frequencies. The ac conductivity obeys the relation σ_ac(ω)=Aω ^S over a considerable range of low temperatures. Values of exponent S are nearly equal to unity at about 78 K and the values decrease non-linearly with the increase of temperature. Values of the number density of states at Fermi level (N(E _F)) have been evaluated at 80 K assuming values of electron wave function decay constant α to be 0.5 (Å)^?1. Values of N(E _F) have the order 10²⁰ which are well within the range suggested for localized states. Present values of N(E _F) are smaller than those for tungsten phosphate glasses.     

Scattering the Geometry of Weighted Graphs

Given two weighted graphs (X, b_k, m_k), k =?1,2 with b₁ ～ b₂ and m₁ ～ m₂, we prove a weighted L¹-criterion for the existence and completeness of the wave operators W_±(H₂, H₁, I_1,2), where H_k denotes the natural Laplacian in ?²(X, m_k) w.r.t. (X, b_k, m_k) and I_1,2 the trivial identification of ?²(X, m₁) with ?²(X, m₂). In particular, this entails a general criterion for the absolutely continuous spectra of H₁ and H₂ to be equal.