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.     

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.     

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 →∞.     

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.     

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.     

Hypersurfaces Satisfying <Emphasis Type="BoldItalic">τ</Emphasis><Subscript><Emphasis Type="BoldItalic">2</Emphasis></Subscript><Emphasis Type="BoldItalic">(ϕ) = ητ(ϕ)</Emphasis> in Pseudo-Riemannian Space Forms

In this paper, we derived the equations for the hypersurface \({M^{n}_{r}}\) of a pseudo-Riemannian space form \(N^{n+1}_{q}(c)\) to satisfy τ ₂(?) = η τ(?) (η a constant) with τ(?) and τ ₂(?) be the tension and bitension fields of \({M^{n}_{r}}\). As applications, we prove that a hypersurface \({M^{n}_{r}}\) satisfying τ ₂(?) = η τ(?) in \(N^{n+1}_{q}(c)\) has constant mean curvature, under the assumption that \({M^{n}_{r}}\) has diagonalizable shape operator with at most three distinct principal curvatures. Then, using this result, we classify partially such hypersurface. We also make a preliminary study of hypersurfaces satisfying τ ₂(?) = f τ(?) with f be function.     

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.     

Decoherence control mechanisms of a charged magneto-oscillator in contact with different environments

In this work, we consider two different techniques based on reservoir engineering process and quantum Zeno control method to analyze the decoherence control mechanism of a charged magneto-oscillator in contact with different type of environment. Our analysis reveals that both the control mechanisms are very much sensitive on the details of different environmental spectrum (J?(ω)), and also on different system and reservoir parameters, e.g., external magnetic field (r _c ), confinement length (r ₀), temperature (T), cut-off frequency of reservoir spectrum (ω _cut ), and measurement interval (τ). We also demonstrate the manipulation scheme of the continuous passage from decay suppression to decay acceleration by tuning the above mentioned system or reservoir parameters, e.g., r _c , r ₀, T and τ.     

Density functional study of $$\hbox {AgScO}_2$$: Electronic and optical properties

Dielectric relaxation studies of binary (jk) polar mixtures of tetrahydrofuran with N-methyl acetamide, N,N-dimethyl acetamide, N-methyl formamide and N,N-dimethyl formamide dissolved in benzene(i) for different weight fractions (w _{j k} ’s) of the polar solutes and mole fractions (x _j ’s) of tetrahydrofuran at 25 ^°C are attempted by measuring the conductivity of the solution under 9.90 GHz electric field using Debye theory. The estimated relaxation time (τ _{j k} ’s) and dipole moment (μ _{j k} ’s) agree well with the reported values signifying the validity of the proposed methods. Structural and associational aspects are predicted from the plot of τ _{j k} and μ _{j k} against x _j of tetrahydrofuran to arrive at solute–solute (dimer) molecular association upto x _j =0.3 of tetrahydrofuran and thereafter solute–solvent (monomer) molecular association upto x _j =1.0 for all systems except tetrahydrofuran + N,N-dimethyl acetamide.     

“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.     

Effect of charge scattering anisotropy on the thermoelectric properties of the (Bi,Sb)<Subscript>2</Subscript>(Te,Se,S)<Subscript>3</Subscript> solid solutions

An analysis is made of the thermoelectric and galvanomagnetic properties of solid solutions based on bismuth and antimony chalcogenides (Bi,Sb)₂(Te,Se,S)₃ with n-and p-type conductivities and different substitutions in the Bi₂Te₃ sublattices. It is shown that the thermoelectric efficiency Z is observed to increase in compositions with a low carrier scattering anisotropy in the reflection plane. The relaxation time tensor component τ ₃₃ along the trigonal direction perpendicular to the crystal growth axis is found to decrease as compared to the components along the binary (τ ₁₁) and bisector (τ ₂₂) directions.     

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.     

Meixner Class of Non-Commutative Generalized Stochastic Processes with Freely Independent Values I. A Characterization

Let T be an underlying space with a non-atomic measure σ on it (e.g. \({T=\mathbb R^d}\) and σ is the Lebesgue measure). We introduce and study a class of non-commutative generalized stochastic processes, indexed by points of T, with freely independent values. Such a process (field), ω = ω(t), \({t\in T}\) , is given a rigorous meaning through smearing out with test functions on T, with \({\int_T \sigma(dt)f(t)\omega(t)}\) being a (bounded) linear operator in a full Fock space. We define a set CP of all continuous polynomials of ω, and then define a non-commutative L ²-space L ²(τ) by taking the closure of CP in the norm \({\|P\|_{L^2(\tau)}:=\|P\Omega\|}\) , where Ω is the vacuum in the Fock space. Through procedure of orthogonalization of polynomials, we construct a unitary isomorphism between L ²(τ) and a (Fock-space-type) Hilbert space \({\mathbb F=\mathbb R\oplus\bigoplus_{n=1}^\infty L^2(T^n,\gamma_n)}\) , with explicitly given measures γ _n . We identify the Meixner class as those processes for which the procedure of orthogonalization leaves the set CP invariant. (Note that, in the general case, the projection of a continuous monomial of order n onto the n ^th chaos need not remain a continuous polynomial.) Each element of the Meixner class is characterized by two continuous functions λ and η ≥ 0 on T, such that, in the \({\mathbb F}\) space, ω has representation \({\omega(t)=\partial_t^\dagger+\lambda(t)\partial_t^\dagger\partial_t+\partial_t+\eta(t)\partial_t^\dagger\partial^2_t}\) , where \({\partial_t^\dagger}\) and ? _t are the usual creation and annihilation operators at point t.     

Fluctuations in the paraphase of improper ferroelastics taking into account indirect interactions through the field of elastic deformations

The effect of indirect interactions (through the field of elastic deformations) on the temperature dependences of a two-point correlator of the order parameter of an improper ferroelastic is studied theoretically taking into account the interaction of fluctuations at different spatial points with one another and with defective elastic fields. The latter are accounted for by using a phenomenological field of the sources of defective elastic fields. Analysis is carried out using diagrammatic expansions followed by a transition to the Dyson equation. It is proposed that the Dyson equation be approximately solved nonperturbatively using the ansatz for an exact two-point Green function of the form G_int(k)=T/[α_ij(τ)k _i k _j +β(τ)]. Such an approach makes it possible to reduce the problem to solving a system of nonlinear algebraic equations, which can effectively be solved by numerical methods. The aggregate of the assumptions made is equivalent to the mean field theory, which, however, cannot be reduced in the present case to the Ginzburg-Landau theory in view of the essentially nonlocal character of the indirect interaction via the field of elastic deformations. The results of numerical calculations are considered for a defect-free Hg₂Cl₂ crystal, for which it is shown that parameters of dispersion α_ij acquire a substantial temperature dependence in a temperature range much broader than the width of the critical region of the given crystal.     

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.     

ESR-Linienbreite der Ionen der Eisengruppe in Lösungen

Electron spin resonance linewidths of ions belonging to the first transition group with quenched orbital angular momentum are calculated using a modified relaxationmatrix theory including third and fourth order perturbation terms. We base our calculation on a Hamiltonian, which depends on electron spin, nuclear spin, orbital angular momentum, rotation of the whole complex, and vibration of the ligands. Quadrupol effects, intermolecular electron-electron and electron-nucleus interactions are neglected. The results show that the well-known formula of the transverse relaxation time derived by using the spin-Hamiltonian is correct, if first the contribution of the rotational spin orbit process is taken in consideration and second the rotational correlation timeτ _c is replaced byτ _v =(1/τ _c +1/τ(0))^?1. 1/τ(0) describes the linewidth of the lowest energy value of the electrostatic energy of unpaired electrons in the ligand field. The linewidth arises from the normal modes of the complex; the calculation gives τ(0)=l0^?11...10^?12 sec.     

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.