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.     

Investigation of zero-frequency solutions to the pion dispersion equation

The instability of nuclear matter is considered for the case where it is generated by the vanishing of the frequencies of collective excitations belonging to specific types (specifically, excitations that have the pion quantum numbers J ^π = 0^?). The behavior of zero-frequency solutions to the pion dispersion equation is analyzed versus the strength G′ of spin—isospin particle—hole interaction. It is shown that there exists a strength value G′_tr (|G′_tr| ? 1) such that, for G′ < G′_tr, zero-frequency solutions are excitations of the ω _P type, while, for G′ ≥ G′_tr, such solutions are excitations of the ω _c type. Excitations of the ω _P type for G′ < ?1 describe the instability of nuclear matter against small density fluctuations (Pomeranchuk’s instability), while excitations of the ω _c type are responsible for the instability associated with pion condensation at G′ ≈ 2. For stable nuclear matter, the solutions ω _P(κ) and ω _c (κ) lie on unphysical sheets of the complex plane of frequency.     

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.     

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.     

Influence of pressure on electronic and optical properties of phosphorus-doped ZnO

In this work, the geometrical, electronic structure and optical properties of P-doped ZnO under high pressures have been investigated using first-principles methods. The pressure effects on the lattice parameters, electronic band structures, and partial density of states of crystalline P-doped ZnO are calculated up to 8 GPa. Moreover, the evolution of the dielectric function, absorption coefficient (αω)), reflectivity (R(ω)), and the real part of the refractive index (n(ω)) at high pressure are also presented.     

Electronic and optical properties of Fe<Subscript>2</Subscript>SiO<Subscript>4</Subscript> under pressure effect: ab initio study

We report first-principles studies the structural, electronic, and optical properties of the Fe₂SiO₄ fayalite in orthorhombic structure, including pressure dependence of structural parameters, band structures, density of states, and optical constants up to 30 GPa. The calculated results indicate that the linear compressibility along b axis is significantly higher than a and c axes, which is in agreement with earlier work. Meanwhile, the pressure dependence of the electronic band structure, density of states and partial density of states of Fe₂SiO₄ fayalite up to 30 GPa were presented. Moreover, the evolution of the dielectric function, absorption coefficient (α(ω)), reflectivity (R(ω)), and the real part of the refractive index (n(ω)) at high pressure are also presented.     

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 →∞.     

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.     

Waves in a superlattice with anisotropic inhomogeneities

Dependences of the dispersion laws and damping of waves in an initially sinusoidal superlattice on inhomogeneities with anisotropic correlation properties are studied for the first time. The period of the superlattice is modulated by the random function described by the anisotropic correlation function K_?(r) that has different correlation radii, k _∥ ^?1 and k _⊥ ^?1 , along the axis of the superlattice z and in the plane xy, respectively. The anisotropy of the correlation is characterized by the parameter λ=1?k_⊥/k_∥ that can change from λ=0 to λ=1 when the correlation wave number k⊥ changes from k_⊥=k_∥ (isotropic 3D inhomogeneities) to k_⊥=0 (1D inhomogeneities). The correlation function of the superlattice K(r) is developed. Its decreasing part goes to the asymptote L that divides the correlation volume into two parts, characterized by finite and infinite correlation radii. The dependences of the width of the gap in the spectrum at the boundary of the Brillouin zone δν and the damping of waves ξ on the value of λ are studied. It is shown that decreasing L leads to the decrease of δν, and increase of ξ, with the increase of λ.     

Effect of the hexagonal warping on the dynamical conductivity of surface states in a topological insulator

We report on the effect of hexagonal warping on the dynamical conductivity of the surface states of a topological insulator in the presence of nonmagnetic impurities. It is found that the photon energy dependent conductivities are determined by a polarization-function-liked term,  Π₂ (q,ω), which contains a velocity term corresponding to the difference of group velocities between the two states due to an electron-impurity scattering. This is different from the conductivity of 2-dimentional electron systems where the conductivity depends on the inverse imaginary part of the dielectric function Im [1/κ(q,ω)]. We present both the real part and imaginary part of the polarization function with different warping strength. It is found that the warping strength can both enhance single particle excitations (SPEs) and suppress the screening effect of electrons. As a result the inverse scattering time is enhanced by up to about two orders of magnitudes. The real part of the longitudinal conductivity of the intra-band process is analog to the case with a conductivity of σ ~ μδ(ω). The broadening of the spectrum in the low energy is not only determined by chemical potential, but also dependent on the warping strength. At higher frequency, the real part of conductivity shows a jump at the threshold photon energy of μ, where the inter-band contribution takes over.     

Structural features and the microscopic dynamics of the three-component Zr<Subscript>47</Subscript>Cu<Subscript>46</Subscript>Al<Subscript>7</Subscript> system: Equilibrium melt,supercooled melt,and amorphous alloy

The structural and dynamic properties of the three-component Zr₄₇Cu₄₆Al₇ system are subjected to a molecular dynamics simulation in the temperature range T = 250–3000 K at a pressure p = 1.0 bar. The temperature dependences of the Wendt–Abraham parameter and the translation order parameter are used to determine the glass transition temperature in the Zr₄₇Cu₄₆Al₇ system, which is found to be T_c ≈ 750 K. It is found that the bulk amorphous Zr₄₇Cu₄₆Al₇ alloy contains localized regions with an ordered atomic structures. Cluster analysis of configuration simulation data reveals the existence of quasi-icosahedral clusters in amorphous metallic Zr–Cu–Al alloys. The spectral densities of time radial distribution functions of the longitudinal (C?_L(k, ω)) and transverse (C?_T(k, ω)) fluxes are calculated in a wide wavenumber range in order to study the mechanisms of formation of atomic collective excitations in the Zr₄₇Cu₄₆Al₇ system. It was found that a linear combination of three Gaussian functions is sufficient to reproduce the (C?_L(k, ω)) spectra, whereas at least four Gaussian contributions are necessary to exactly describe the (C?_T(k, ω)) spectra of the supercooled melt and the amorphous metallic alloy. It is shown that the collective atomic excitations in the equilibrium melt at T = 3000 K and in the amorphous metallic alloy at T = 250 K are characterized by two dispersion acoustic-like branches related with longitudinal and transverse polarizations.     

Singular Resonance in Fluctuation-Induced Electromagnetic Phenomena at the Rotation of a Nanoparticle near the Surface of a Condensed Medium

It has been shown that the rotation of a spherical nanoparticle with the radius R near the surface of a semi-infinite homogeneous medium can result in singular resonance in fluctuation-induced electromagnetic phenomena (Casimir force, Casimir friction, and radiative heat generation). Fluctuation electromagnetic effects increase strongly near this resonance even in the presence of dissipation in the system. The resonance occurs at distances of the particle from the surface d < d₀R(3/4ε″₁(ω₁)ε″₂ (ω₂))^1/3 (where ε″_i(ω_i) is the imaginary part of the dielectric function of the particle or the medium at the frequency of a surface phonon or plasmon polariton ω_i), when the rotation frequency coincides with poles in the photon generation rate at Ω ≈ ω₁ + ω₂. These poles are due to the multiple scattering of electromagnetic waves between the particle and surface under conditions of the anomalous Doppler effect. These poles exist even in the presence of dissipation. At d < d₀, depending on the particle rotation frequency, the Casimir force can change sign; i.e., the attraction of the particle to the surface changes to repulsion. The results can be important for the development of experimental methods for the detection of quantum friction.     

Fine Structure of Beta Decay Strength Function and Anisotropy of Isovector Nuclear Dencity Component Oscillations in Deformed Nuclei

The experimental measurement data on the fine structure of beta-decay strength function S_β(E) in spherical, transitional, and deformed nuclei are analyzed. Modern high-resolution nuclear spectroscopy methods made it possible to identify the splitting of peaks in S_β(E) for deformed nuclei. By analogy with splitting of the peak of E1 giant dipole resonance (GDR) in deformed nuclei, the peaks in S_β(E) are split into two components from the axial nuclear deformation. In this report, the fine structure of S_β(E) is discussed. Splitting of the peaks connected with the oscillations of neutrons against protons (E1GDR), of proton holes against neutrons (peaks in S_β(E) of β⁺/EC-decay), and of protons against neutron holes (peaks in S_β(E) of β^–-decay) is discussed.     

Control of the perturbation-wave-vector range of modulation instability of dispersive electromagnetic waves in the nonlocal Josephson electrodynamics of a thin superconducting film

Modulation instability of dispersive electromagnetic waves propagating through a Josephson junction in a thin superconducting film is investigated in the framework of the nonlocal Josephson electrodynamics. A dispersion relation is found for the time increment of small perturbations of the amplitude. For dispersive waves, it is first established that spatial nonlocality suppresses the modulation instability in the range of perturbation wave vectors 0≤Q≤Q_B1(k), i.e., in the long-wavelength range of experimental interest. The modulation instability range Q_B1(k)<Q<Q_B2(k, A, L) can be controlled (which is a unique possibility) by varying a dispersion parameter, namely, the wave vector k [or the frequency ω(k)] of linear-approximation waves. In the wave-vector ranges 0≤Q≤Q_B1(k) and Q≤Q_B2(k, A, L), waves are shown to be stable.     

The shape of the giant dipole resonance for light nuclei

A complete spectrum of the giant dipole resonance is calculated taking into account the finite depth of the single particle potential. The mixing of the one particle-one hole excitations because of residual interactions is treated in the time-dependent Hartree-Fock approximation. If the interaction is approximated by a separable potential a general formula can be derived, which gives the total dipole excitation cross section σ(E) in terms of the simple shell-model cross section σ₀(E). Numerical results are given for O¹⁶ and C¹² by evaluating σ₀(E) in a square well potential.     

Medium polarization and pairing in asymmetric nuclear matter

The many-body theory of asymmetric nuclear matter is developed beyond the Brueckner–Hartree–Fock approximation to incorporate the medium polarization effects. The extension is performed within the Babu–Brown induced interaction theory. After deriving the particle–hole interaction in the form of Landau–Migdal parameters, the effects of the induced component on the symmetry energy are investigated along with the screening of ¹ S ₀ proton–proton and ³ PF ₂ neutron–neutron pairing, which are relevant for the neutron-star cooling. The crossover from repulsive (screening) to attractive (anti-screening) interaction going from pure neutron matter to symmetric nuclear matter is discussed.     

“Negative” gap in the spectrum of localized states of (In<Subscript>2</Subscript>O<Subscript>3</Subscript>)<Subscript>0.9</Subscript>(SrO)<Subscript>0.1</Subscript>

The reflection R(?ω), transmission t(?ω), absorption α(?ω), and refraction n(?ω) spectra of polycrystalline In₂O₃–SrO samples with low optical transparency, which contain In₂O₃ and In₂SrO₄ crystallites with In₄SrO_{6 + δ} interlayers, are examined. In the region of small ?ω values, the reflection coefficient decreases as the resistance of samples saturated with oxygen increases. Spectral dependences n(?ω) and α(?ω) are calculated using the classical electrodynamics relations. The results are compared to the data based on the t(?ω) spectra. The calculated absorption spectra are interpreted within the model with an overlap of tails of the density of states in the valence band and in the conduction band. A “negative” gap E _gn in the density of states with a width from–0.12 to–0.47 eV is formed in highly disordered samples in this model. It is demonstrated that the high density of defects and the band of deep acceptor states of strontium in the major matrix In₂O₃ phase are crucial to tailing of the absorption edge and its shift toward lower energies. The direct gap E _gd = 1.3 eV corresponding to the In₂SrO₄ phase is determined. The energy band diagram and the contribution of tunneling, which reduces the threshold energy for interband optical transitions, are discussed.     

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.