TN approximation to reflected slab and computation of the critical half thicknesses

The criticality solution to one-speed neutron transport equation using the T_N approximation is described for reflected slab. In the solution, Marshak type boundary condition is used. The critical half thicknesses are computed for different values of c and reflection coefficients. Computations are made by using the both T_N and P_N approximation for the comparison.     

Inverse solutions to radiative-transfer problems with partially transparent boundaries and diffuse reflection

Analytical techniques are used to solve a class of inverse radiative-transfer problems relevant to finite and semi-infinite plane-parallel media. While the assumption of isotropic scattering is made, diffuse reflection is allowed at the surface, for the semi-infinite case, and at both surfaces for the case of a finite layer. For the general case based on a semi-infinite medium, a cubic algebraic equation is used to define the basic result, but for the specific case of a semi-infinite medium illuminated by a constant incident distribution of radiation, very simple exact expressions are developed for the albedo for single scattering ? and the coefficient for diffuse reflection ρ. Analytical results are also developed (again in terms of a cubic algebraic equation) for the case of a finite layer with equal reflection coefficients relevant to the two surfaces. For the general case of a finite layer with unequal reflection coefficients, two specific formulations are given. The first algorithm is based on a system of three quadratic algebraic equations for the two reflection coefficients ρ₁ and ρ₂ and the single-scattering albedo ?. Secondly, an elimination between these three algebraic equations is carried out to yield two coupled algebraic equations for ρ₁ and ρ₂ plus an explicit expression for ? in terms of ρ₁ and ρ₂. In addition, an exact expression for τ₀, the optical thickness of the finite layer, is developed in terms of ?, ρ₁ and ρ₂. As is typical with the considered class of inverse problems in radiative transfer, all surface quantities are either specified or considered available from experimental measurements. All basic results are tested numerically.     

Exp-function method for N-soliton solutions of nonlinear evolution equations in mathematical physics

In this Letter, the Exp-function method is generalized to construct N-soliton solutions of a KdV equation with variable coefficients. As a result, 1-soliton, 2-soliton and 3-soliton solutions are obtained, from which the uniform formula of N-soliton solutions is derived. It is shown that the Exp-function method may provide us with a straightforward and effective mathematical tool for generating N-soliton solutions of nonlinear evolution equations in mathematical physics.     

Cavitation in holographic sQGP

We study the possibility of cavitation in the non-conformal N=^2?SU(N) theory which is a mass deformation of N=4SU(N) Yang-Mills theory. The second order transport coefficients are known from the numerical work using AdS/CFT by Buchel and collaborators. Using these and the approach of Rajagopal and Tripuraneni, we investigate the flow equations in a (1+1)-dimensional boost invariant set up. We find that the string theory model does not exhibit cavitation before phase transition is reached. We give a semi-analytic explanation of this finding.     

Resonant Bragg reflection from quantum-well structures

The resonant spectra of light reflected and transmitted by a heterostructure with a finite system of equidistant quantum wells have been calculated. Recurrence relations have been derived connecting the amplitude reflection coefficients from N and N - 2 quantum wells, and analytical properties of the reflection coefficient as a function of the complex frequency ω have been established. A method has been proposed which allows one to find complex frequencies of coupled exciton-photon nonstationary modes, or exciton-polaritons. It has been shown that the resonant Bragg structures represent a particular case where among N eigenmodes only one is radiative.     

Collective coupling of randomly dispersed oscillators with cavities filled with zero-index metamaterials

In cavity quantum electrodynamics, it is hard to enhance the coupling strength between quantum dot (QD) and cavity, owing to the limited choice of QDs and the positional uncertainty brought by the inhomogeneous cavity fields. In this paper, we randomly distribute N oscillators with oscillating strength G = G ₀ into a cavity filled with a zero-index metamaterial (ZIM). Because of the enhanced uniform fields, each oscillator couples to the field maximum and the N oscillators are equivalent to one oscillator with effective N G ₀. This provides a way to enhance the coupling strength just by adding the number of QDs. Both simulation and experiment demonstrate the adjustable coupling strength in ZIM-filled cavities.     

Exact local in time evolution equations for macroobservables

By introducing an evolution equation for the generalized Gibbs state σ(t), the N-particle distribution function is expressed as a linear functional of σ(t). Exact equations local in time for the time evolution of macroobservables are obtained. The kinetic coefficients appear as the fixed point of a conveniently defined microscopic expression which may be considered as a natural extension of the Kubo formula.     

Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods

A robust methodology is presented for efficiently solving partial differential equations using Chebyshev spectral techniques. It is well known that differential equations in one dimension can be solved efficiently with Chebyshev discretizations, O(N) operations for N unknowns, however this efficiency is lost in higher dimensions due to the coupling between modes. This paper presents the “quasi-inverse“ technique (QIT), which combines optimizations of one-dimensional spectral differentiation matrices with Kronecker matrix products to build efficient multi-dimensional operators. This strategy results in O(N^2D?1) operations for N^D unknowns, independent of the form of the differential operators. QIT is compared to the matrix diagonalization technique (MDT) of Haidvogel and Zang [D.B. Haidvogel, T. Zang, The accurate solution of Poisson’s equation by expansion in Chebyshev polynomials, J. Comput. Phys. 30 (1979) 167–180] and Shen [J. Shen, Efficient spectral-Galerkin method. II. Direct solvers of second- and fourth-order equations using Chebyshev polynomials, SIAM J. Sci. Comp. 16 (1) (1995) 74–87]. While the cost for MDT and QIT are the same in two dimensions, there are significant differences. MDT utilizes an eigenvalue/eigenvector decomposition and can only be used for relatively simple differential equations. QIT is based upon intrinsic properties of the Chebyshev polynomials and is adaptable to linear PDEs with constant coefficients in simple domains. We present results for a standard suite of test problems, and discuss of the adaptability of QIT to more complicated problems.     

Analytical solution of the direct problem of ellipsometry for some profiles of optical constants of inhomogeneous layers

Differential equations that describe the reflection of polarized light from an optically inhomogeneous medium are considered. In the approximation of small variations of the refractive index, analytical expressions for the reflection coefficients are obtained for both types of polarization for the exponential and harmonic profiles of the optical constants. The accuracy of the obtained expressions is estimated by numerical simulation. It is found that analytical formulas describe well the behavior of the ellipsometric parameters of periodic structures based on Hg_1–xCd_xTe with a sinusoidal profile of the refractive index.     

Solutions to the reflection equation and integrable systems for N = 2 SQCD with classical groups

Integrable systems underlying the Seiberg-Witten solutions for the N = 2 SQCD with gauge groups SO(n) and Sp(n) are proposed. They are described by the inhomogeneous XXX spin chain with specific boundary conditions given by reflection matrices. We attribute reflection matrices to orientifold planes in the brane construction and briefly discuss its possible deformations.     

Magnetooptical properties of a ferromagnetic superlattice

Transmission and reflection of a normally incident wave from a magnetic superlattice consisting of 2N ferromagnetic layers with alternating orientation of the magnetization vector are considered. The characteristic matrix of a superlattice relating wave amplitudes at the entrance to the system and at the exit from it is calculated in the closed form and Jones matrices determining all the basic magnetooptical characteristics of the structure (transmission and reflection coefficients, the degree of polarization of transmitted and reflected waves, and so on) are constructed. A significant dependence of these characteristics on the number of layers is demonstrated.     

Conductivity of single-walled carbon nanotubes

In a system of N interacting single-level quantum dots (QDs), we study the relaxation dynamics and the current–voltage characteristics determined by symmetry properties of the QD arrangement. Different numbers of dots, initial charge configurations, and various coupling regimes to reservoirs are considered. We reveal that effective charge trapping occurs for particular regimes of coupling to the reservoir when more than two dots form a ring structure with the C_N spatial symmetry. We reveal that the effective charge trapping caused by the C_N spatial symmetry of N coupled QDs depends on the number of dots and the way of coupling to the reservoirs. We demonstrate that the charge trapping effect is directly connected with the formation of dark states, which are not coupled to reservoirs due to the system spatial symmetry C_N. We also reveal the symmetry blockade of the tunneling current caused by the presence of dark states.     

Solution of the three-dimensional problem of wave diffraction by an ensemble of objects

The pattern equations method is extended to solving three-dimensional problems of wave diffraction by an ensemble of bodies. The method is based on the reduction of the initial problem to a system of N (N is the number of scatterers in the ensemble) integro-operator equations of the second kind for the scattering patterns of scatterers. With the use of the series expansions of the scattering patterns in angular spherical harmonics, the problem is reduced to an algebraic system of equations in the expansion coefficients. An explicit (asymptotic) solution to the problems is obtained in the case when the scattering bodies are separated by sufficiently long distances. It is shown that the method can be used to model the characteristics of wave scattering by complex-shaped bodies.     

Connection between the immersing and transfer-matrix methods in one-dimensional scattering problems

We show that application of the immersing and transfer-matrix methods to one-dimensional problems of particles scattering leads to the system of two linear equations for the functions F and Φ expressed by means of the transmission and reflection amplitudes. The expressions of these functions are derived. The offered method is illustrated by the finding of transmission and reflection coefficients for the potential barrier with a constant height. The developed method can be applied in solving the quasi-one-dimensional and two-dimensional problems of scattering.     

Anisotropic clusters with itinerant charge carriers in the layered EuBaCo<Subscript>1.9</Subscript>O<Subscript>5.36</Subscript> cobaltite

The anisotropy of reflection spectra is studied for the single crystals of layered EuBaCo_1.9O_5.36 cobaltite within the temperature range of 80–295 K. The results involving the comparison with the magnetic and transport characteristics are analyzed. In the reflection spectra from the (001) and (120) planes measured at T = 295 K (below the temperature corresponding to the transition to the semiconducting state, T_MI = 345 K), a contribution from itinerant charge carriers has been revealed. This contribution is associated with the existence of an inhomogeneous charge state. In the reflection spectrum from the (120) plane, the contribution from itinerant charge carriers holds down to T = 80 K. The difference between the reflection spectra from different planes and different characters of their changes with the temperature are attributed to the anisotropy of the clusters with itinerant charge carriers.     

Moving potential for Dirac and Klein–Gordon equations

Using the Lorentz transformation, the Klein–Gordon and Dirac equations with moving potentials are reduced to one standard where the potential is time-independent. As application, the reflection and transmission coefficients are determined by considering the moving step with a constant velocity v. It has been found that R ± T = 1 only at x = vt. The problem of massless (2 + 1) Dirac particle is also considerered.     

Integral equations for the scattering of N identical particles

Integral equations are obtained for the scattering of N identical particles using a form of the N-particle scattering equations derived previously. The equations couple together only transition operators between physical two cluster channels, the breakup amplitudes being expressed in terms of quadratures over two-cluster amplitudes. The kernel of the equations becomes connected after a single iteration. The number of coupled equations for identical particles is $\text{1}\text{2}\text{N}\text{or}\text{1}\text{2}\text{(N?1)}$ when N is even or odd respectively.     

Exciton capture and thermal escape in InAs dot-in-a-well laser structures

The photoluminescence (PL), its temperature and power dependences have been studied in InAs quantum dots (QDs) embedded in asymmetric In_xGa_1?y As/GaAs quantum wells (QWs) with variable In_xGa_1?x As compositions in the capping layer. Three stages for thermally activated decay of QD PL intensity have been revealed. A set of rate equations for exciton dynamics (relaxation into QWs and QDs, and thermal escape) are solved to analyze the mechanism of PL thermal decay. The variety of PL intensities and peak positions, as well as the activation energies of PL intensity decay in DWELL structures with different compositions of a capping layer are discussed.     

Tunneling of an energy eigenstate through a parabolic barrier viewed from Wigner phase space

We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients R or T are then given by the total weight of all classical phase-space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function.