Many-body effects on the width of the band gap in Bi2Te2X (X = Te, Se, S) topological insulators

The spectrum of quasiparticles of Bi₂Te₂X (X = Te, Se, S) three-dimensional topological insulators has been theoretically studied in the GW approximation with the inclusion of the spin-orbit interaction in the construction of the Green’s function and self-energy. It has been shown that many-body corrections to the Kohn-Sham states in Bi₂Te₂X increase the fundamental band gap similar to conventional semiconductors. However, the band gap at the Γ point decreases in this case. Gaps in the quasiparticle spectrum obtained in agreement with the experimental data correspond to the difference between the minimum of the conduction band, which is located on the Γ-Z line, and the maximum of the valence band, which lies beyond the symmetric directions in the mirror plane.     

On the effect of the width of the scattering indicatrix on the dispersion of photon density waves in a strongly scattering medium

The dispersion of photon density waves in strongly scattering media with different widths of the scattering indicatrix is studied by the spherical harmonics method using approximations of various orders (up to the P ₇ approximation inclusive). It is shown that, beginning from the P ₃ approximation, the reduction in the velocity of photon density waves that is characteristic of the P ₁ approximation is eliminated and, independently of the width of the scattering indicatrix in the region of modulation frequencies exceeding 10¹⁰ Hz, the velocity of photon density waves asymptotically approaches the speed of light. Our study of the damping of photon density waves has shown that the formula obtained previously for the calculation of the damping coefficient (Imk(μ _s ^′ , ω)) as a function of the transport scattering coefficient and the velocity is valid at Imk ≤ μ_s (μ_s is the light scattering coefficient). The maximum growth in the damping coefficient of photon density waves with a further increase in the frequency is limited by the value of the light scattering coefficient Imk _max ≈ μ_s.     

Properties of quasiparticle excitations in FeCo ferromagnetic alloy

This paper reports on the results of ab initio spin-polarized GW calculations of quasiparticle properties, such as the spectral weight, the lifetime, the velocity, and the mean free path, for the FeCo ferromagnetic alloy and its components. The contribution of the localized d states to the above characteristics has been analyzed. The spin asymmetry of the properties of quasiparticle excitations, which is responsible for the spin filter effect observed in experiments, has been investigated. The contributions to the mean free path from the electron scattering processes, which are disregarded within the framework of the GW approximation, have been estimated from a comparison with experimental data.     

Neutron scattering in a Leibfried-Brenig spectrum space lattice

The classical high-temperature limit of the pair self-correlation function for a system of harmonic oscillators as introduced by Sunakawaet al. is applied to a lattice whose vibrational spectrum is described by a Leibfried-Brenig approximation. The resulting neutron scattering cross-section is discussed qualitatively; it is shown that the principle of detailed balance is fulfilled.     

The GW plus cumulant method and plasmonic polarons: application to the homogeneous electron gas*

We study the spectral function of the homogeneous electron gas using many-body perturbation theory and the cumulant expansion. We compute the angle-resolved spectral function based on the GW approximation and the “GW plus cumulant” approach. In agreement with previous studies, the GW spectral function exhibits a spurious plasmaron peak at energies 1.5ω_pl below the quasiparticle peak, ω_pl being the plasma energy. The GW plus cumulant approach, on the other hand, reduces significantly the intensity of the plasmon-induced spectral features and renormalizes their energy relative to the quasiparticle energy to ω_pl. Consistently with previous work on semiconductors, our results show that the HEG is characterized by the emergence of plasmonic polaron bands, that is, broadened replica of the quasiparticle bands, red-shifted by the plasmon energy.     

A 90° laser scattering experiment for measuring temperature and density of ions and electrons in a cold dense theta pinch plasma

In a 90° scattering experiment performed on a plasma with a density of some 10¹⁷cm^?3 and a temperature of some eV a scattering spectrum is expected which consists essentially of an intense central part and two very weak satellite peaks. In this investigation the spectrum of the central part (ion line) was resolved. From the ion line alone which was in good agreement with calculated spectra, the ion temperature, electron temperature and electron density were determined. At some plasma parameters only a few particles were included in the Debye volume. Also in these cases no deviations from calculated spectra have been observed. In addition the position and half-width of the satellites were measured. The position of the satellites yields an independent value of the electron density which agrees very well with that determined from the ion line. The half-width of the satellites was much broader than expected theoretically due to fluctuations of the electron density within the scattering volume. The measurement was performed on a theta pinch plasma. The energy of the condensor bank was 7.5 kJ, the voltage 18 kV. As a light source aQ-switch laser was used with a power of about 100 MW. Because of beam stops to prevent stray light only a fourth of the whole power reached the plasma.     

Eigenvalue spectrum with chebyshev polynomial approximation of the transport equation in slab geometry

Using certain well-known properties of chebyshev polynomials, a simple and highly efficient approach to evaluate eigenvalue in radiation transport is presented. The spectrum of eigenvalues has been studied for slabs with isotropic scattering of different magnitudes of the cross section parameter c (i.e., the mean number of neutrons emitted per collision). It is shown that in the presence of the chebyshev polynomial approximation (T_N) there are both discrete and continuum of eigenvalues. It is found that the T_N method gives very good agreement with conventional spherical harmonics approximation (P_N).     

Bulk plasma waves in a randomly inhomogeneous conductor

The modification of the spectrum and damping of bulk plasma waves due to three-dimensional random inhomogeneities of the density of a degenerate electron gas in a conductor have been investigated using the averaged Green??s function method. The dependences of the frequency and damping of the averaged plasma waves, as well as the position ?? _m and width ???? of the peak of the imaginary part of the Fourier trans-form of the averaged Green??s function, on the wave vector k have been determined in the self-consistent approximation, which makes it possible to take into account multiple scattering of plasma waves by inhomogeneities. It has been found that, in the long-wavelength region of the spectrum, the decrease revealed in the frequency of the plasma waves is caused by the inhomogeneities, which agrees qualitatively with the behavior of the position of the peak ?? _m . In the range of large values of the correlation length of inhomogeneities and small values of k, the damping of the plasma waves tends to zero, whereas the width of the peak ???? remains finite, which is due to the nonuniform broadening. A comparison with the data of numerical calculations has been performed.     

Statistical limit in a completely integrable system with deterministic initial conditions

The asymptotic behavior of the solutions of the KdV equation in the classical limit with an oscillating nonperiodic initial function u ₀(x) prescribed on the entire x axis is investigated. For such an initial condition, nonlinear oscillations, which become stochastic in the asymptotic limit t→∞, develop in the system. The complete system of conservation laws is formulated in the integral form, and it is demonstrated that this system is equivalent to the spectral density of the discrete levels of the initial problem. The scattering problem is studied for the Schrödinger equation with the initial potential ?u ₀(x), and it is shown that the scattering phase is a uniformly distributed random quantity. A modified method is developed for solving the inverse scattering problem by constructing the maximizer for an N-soliton solution with random initial phases. A one-to-one relation is established between the spectrum of the discrete levels of the initial state of the system and the spectrum established in phase space. It is shown that when the system passes into the stochastic state, all KdV integral conservation laws are satisfied. The first three laws are satisfied exactly, while the remaining laws are satisfied in the WKB approximation, i.e., to within the square of a small dispersion parameter. The concept of a quasisoliton, playing in the stochastic state of the system the role of a standard soliton in the dynamical limit, is introduced. A method is developed for determining the probability density f(u), which is calculated for a specific initial problem. Physically, the problem studied describes a developed one-dimensional turbulent state in dispersion hydrodynamics.     

Multichannel features of the continuous spectrum of 6He

It is shown that the continuous spectrum of the ⁶He nucleus immediately above the threshold for its breakup into an alpha particle and two neutrons has some features that are not peculiar to the continuous spectrum of binary systems. This spectrum has an infinite degeneracy multiplicity; hence, there exist an infinite number of decay channels even if we fix the angular momentum and the parity of a channel. In states characterized by a fixed value of the grand orbital, the potential energy of the ⁶He nucleus decreases with increasing hyperradius in inverse proportion to its cube. This circumstance is reflected in the behavior of the S-matrix elements for 3 → 3 scattering at low above-threshold energies. Because of the effect of the Pauli exclusion principle, the grand orbital generally ceases to be an appropriate quantum number for classifying decay channels, and the resulting conventional situation requires invoking superpositions of states corresponding to different values of the grand orbital. Within the method of three-cluster hyperharmonics and the approximation of an asymptotic potential, we calculate the eigenphases of the scattering matrix and reveal regularities in the behavior of these phases as functions of energy.     

Study and Characterization of Resonances in the Four-Wave Mixing Signal of a Two-Level System with Intramolecular Coupling

The Liouville formalism in frequency space is used in the present study to investigate the effect of the intramolecular coupling on the four wave mixing signal (FWM) of a two-level system. The internal rovibrational structure is incorporated by including the spin-orbit residual interaction in the total Hamiltonian of the system. The behavior of the FWM signal as a function of the coupling parameters (v and V₀) has been studied. The main properties affected were the permanent and transition dipole moments of the solute molecules when the rotating wave approximation is neglected. Reduced polarization expressions are obtained from the resonant terms and from the larger coherence and population density contributions to the macroscopic polarization, which in turn allows us to characterize individual resonances in the resulting frequency spectrum.     

The method of unitary transformations in the theory of nuclear matter

The theory of nuclear matter is investigated by means of the method of unitary transformations in the special case of point transformations. The general formula for the energy per particle as a function of the density is given in Hartree-Fock approximation being neglected the induced three and more body forces for reasonable correlation functions. This function always shows saturation due to a term proportional tok _F ⁵ in the direct part of the approximation. The physical connexion of this term with the scattering amplitudes of the potential is shown. We point out the equivalence to orderk _F ³ of the energy per particle function of the unitary method with Jastrow and separation methods in their simplest form. The saturation properties are calculated for certain classes of correlations using the realistic potential of Gammel, Christian and Thaler.     

Unconventional application of the two-flux approximation for the calculation of the Ambartsumyan-Chandrasekhar function and the angular spectrum of the backward-scattered radiation for a semi-infinite isotropically scattering medium

It is commonly accepted that the Schwarzschild-Schuster two-flux approximation (1905, 1914) can be employed only for the calculation of the energy characteristics of the radiation field (energy density and energy flux density) and cannot be used to characterize the angular distribution of radiation field. However, such an inference is not valid. In several cases, one can calculate the radiation intensity inside matter and the reflected radiation with the aid of this simplest approximation in the transport theory. In this work, we use the results of the simplest one-parameter variant of the two-flux approximation to calculate the angular distribution (reflection function) of the radiation reflected by a semi-infinite isotropically scattering dissipative medium when a relatively broad beam is incident on the medium at an arbitrary angle relative to the surface. We do not employ the invariance principle and demonstrate that the reflection function exhibits the multiplicative property. It can be represented as a product of three functions: the reflection function corresponding to the single scattering and two identical h functions, which have the same physical meaning as the Ambartsumyan-Chandrasekhar function (H) has. This circumstance allows a relatively easy derivation of simple analytical expressions for the H function, total reflectance, and reflection function. We can easily determine the relative contribution of the true single scattering in the photon backscattering at an arbitrary probability of photon survival Λ. We compare all of the parameters of the backscattered radiation with the data resulting from the calculations using the exact theory of Ambartsumyan, Chandrasekhar, et al., which was developed decades after the two-flux approximation. Thus, we avoid the application of fine mathematical methods (the Wiener-Hopf method, the Case method of singular functions, etc.) and obtain simple analytical expressions for the parameters of the scattered radiation. Note that the simplicity of the expressions is supplemented with unexpectedly high accuracy. The results demonstrate the unknown possibilities offered by the two-flux approximation, which is the simplest approximate method to solve the equations of transport theory. We assume that the method can be employed in the calculations of the angular characteristics of the reflected radiation for media whose single scattering is described using complicated (in comparison with isotropic) laws.     

Continuous spectrum of three-cluster systems

For the example of the ⁵H = ³H + n + n nucleus, the effect of the Pauli exclusion principle on the asymptotic behavior of wave functions for the continuous spectrum of three-cluster systems is studied within a microscopic approach. It is shown that, in the asymptotic limit, the Schrödinger equation for the wave function that describes the relative motion of tritium and two neutrons reduces to the multichannel problem of valence-neutron scattering on the ⁴H subsystem. The single-channel approximation within which the phase shift for neutron scattering on the ⁴H subsystem occurring in the lowest energy state is the only feature that characterizes the continuous spectrum of the ⁵H nucleus is proposed and implemented.     

Structural,electronic, and optical properties of bulk Cu2Se

By using first-principles calculations within the density functional theory and the many-body perturbation theory, we investigate the structural, electronic, and optical properties of bulk Cu₂Se with a recently discovered low-temperature layered configuration. We demonstrate that the effects of the van der Waals forces significantly modify the interlayer binding and distance in the layered Cu₂Se, while the band gap is invariant. Our density functional theory and post-processing GW calculations reveal that for the layered structure, GW correction remedies the serious band-gap underestimation of the density functional theory from 0.12 eV to 0.99 eV. By solving the Bethe–Salpeter equation, we find that the optical gap of the layered Cu₂Se is 0.86 eV, which is in close agreement with previous experimental observations. In addition, we show that the high-temperature fluorite structure has no band gap, even after GW correction, explaining that the band gap controversy among the theories stems from different structural models. This work may serve as an important guide in designing and evaluating photovoltaic devices using Cu₂Se-based materials.     

Extending the applicability of the discrete dipole approximation for multi-scale features on surface

Many problems in science and engineering involve significant physical entities and processes that span a substantial range of dimensions. In the case of characterization of bacteria on growth media using light scattering the length scales of interest can be classified as micro-scale (single bacterium), macro-scale (bacterial colonies of more than 10¹² bacterium that have passed through the exponential growth phase and reached mm size), and the intermediate or meso-scale of several tens of hundreds of bacteria. Light scattering approaches, to be effective in determining physical properties such as morphology and material composition, must comprehend this spectrum of length scales. The discrete dipole approximation (DDA), a powerful modeling tool for rigorous 3-D vector scattering, has shown its capability to predict the light scattering from micro-scale objects. To be able to accommodate meso-scale objects, we need to extend the computational limits of the DDA method such that it could compute object sizes of 10λ-30λ characteristic dimension (i.e. volumes of 10³-10⁴ cubic wavelengths). To accomplish this, an analysis of the DDA method was performed for meso-scale cases of interest especially in biological applications. Based on this study, we propose new Sommerfeld integration paths and a revised iterative algorithm that combine to provide substantial improvements in the size of the computational domain that can be modeled for a given convergence criterion.     

Density of vibrational states in amorphous solid media: Measurement by single-molecule spectroscopy

The energy spectrum of low-frequency vibrational modes in amorphous polyisobutylene doped with chromophore tetra-tert-butylterrylene molecules has been measured. The technique for measuring the spectra of vibrational modes in solid amorphous media by single-molecule spectroscopy is described. The measured spectrum is compared with the data on the density of vibrational states (bosonic peak) in pure polyisobutylene, which were obtained by inelastic neutron scattering. It is shown that incorporation of small amounts of tetra-tert-butylterrylene into polyisobutylene did not significantly change the low-temperature vibrational dynamics of the matrix.     

Removal of inelastic scattering part from Ti2p XPS spectrum of TiO2 by deconvolution method using O1s as response function

Ti2p and O1s XPS spectra of a clean surface of single crystal TiO₂ fractured in situ were taken to study the removal of the inelastic scattering part from the Ti2p spectrum. The features of inelastic scattering peaks in EELS were more influenced by surface than O1s XPS. It indicates that O1s XPS is proper as the response function to deconvolute a Ti2p spectrum. FWHM of the non-energy loss peak of Ti2p_3/2 is smaller than that of O1s. When the raw O1s spectrum is used as the response function, the deconvoluted spectrum has negative intensity values in some regions and beat waves. The replacement of the non-energy loss peak of O1s with narrower Gaussian peak takes off the beat waves. Peak separation of the deconvoluted spectrum reveals that it has six peaks. Two of them are main peaks of Ti2p_3/2 and 2p_1/2. The others are classified into two kinds of satellite peaks, whose energy separation from the main peaks are 3 and 13 eV. Although the latter satellites have been discussed by many authors, the former satellites are first reported here.