Search

We present Bogoliubov's causal perturbative QFT with only one refinement: the creation–annihilation operators at a point, i.e., for a specific momentum, are mathematically interpreted as the Hida operators from the white noise analysis. We leave the rest of the theory completely unchanged. This allows avoiding infrared (and ultraviolet) divergences in the transition to the adiabatic limit for interacting fields and eliminating the free parameters of the theory associated with the choice of normalization in computation of the retarded and advanced parts of causal distributions (corresponding to the freedom in choosing the renormalization scheme). This enhances the predictive power of the theory, and in particular allows deriving nontrivial mass relations. The approach is general and can be applied to investigate any perturbative QFT. [ABSTRACT FROM AUTHOR]

In this paper, we present the Bogoliubov's causal perturbative QFT, which includes only one refinement: the creation-annihilation operators at a point, i.e. for a specific momentum, are mathematically interpreted as the Hida operators from the white noise analysis. We leave the rest of the theory completely unchanged. This allows avoiding infrared — and ultraviolet — divergences in the transition to the adiabatic limit for interacting fields. We present here the analysis of the causal axioms for the scattering operator with the Hida operators as the creation-annihilation operators. [ABSTRACT FROM AUTHOR]

The discrete-time quantum walk (DTQW) with step-dependent (SD) scattering operator is implemented on quantum computer. The probabilities of different states, with their respective fidelities, are calculated. This is done by generalizing the coin with a rotation gate using the quantum gate model. The CNOT gates in the shift operator are replaced with the alternative to CNOT gates Rx(π). They are applied on a quantum device and a quantum simulator (QS). The fidelities varied around 50% and the probability distribution of SD-DTQW for the angle π/4 spread symmetrically, while the step-independent DTQW (SI-DTQW) tended to peak at one side. The symmetric probability distribution of SD-DTQW can help in better control of the walk on QS. In the case of angle π/2, the SI-DTQW spread equally across the states with four peaks, while the SD-DTQW spread with two peaks to one side. [ABSTRACT FROM AUTHOR]

We will present the axioms of Bogoliubov's causal perturbative QFT in which the creation-annihilation operators are interpreted as Hida operators. We will shortly present the results that can be achieved in this theory: (1) removal of UV and IR infinity in the scattering operator, (2) existence of the adiabatic limit for interacting fields in QED, (3) proof that charged particles have nonzero mass, (4) existence of infrared and ultraviolet asymptotics for QED. [ABSTRACT FROM AUTHOR]

We consider the initial-boundary value problem for the nonlinear Klein-Gordon equation posed on a quarter-plane with Dirichlet non zero boundary conditions. We construct the wave and scattering operators for this model in the scattering-supercritical regime. We study the influence of the boundary data on the asymptotic behavior of solutions. We show that if the boundary data has sufficiently slow decay rate, it affects the order of the nonlinearity for which we are able to construct the scattering operator. This suggests a modification for the critical value of the nonlinear term due to the presence of non zero boundary condition. In order to prove our results, we construct an explicit formula for the solutions to corresponding linear Klein-Gordon equation on a quarter-plane. Using this explicit formula, we obtain weighted Sobolev estimates for the solution to the complete nonlinear problem. In order to control the long-time behavior of the solution we find an operator J suitable for our settings, analogous to operator x + i t ∂ x in the case of NLS equation. [ABSTRACT FROM AUTHOR]

We present Bogoliubov's causal perturbative QFT with a single refinement: the creation–annihilation operators at a point, i.e., for a specific momentum, are mathematically interpreted as the Hida operators from the white noise analysis. We leave the rest of the theory completely unchanged. This allows avoiding infrared and ultraviolet divergences in the transition to the adiabatic limit for interacting fields. We present the existence proof for the adiabatic limit for interacting fields in causal QED with Hida operators. This limit exists if and only if the normalization in the Epstein–Glaser splitting of the causal distributions, in the construction of the scattering operator, is "natural,", which eliminates the arbitrariness in choosing the splitting that makes the theory definite, with its predictive power considerably strengthened. We present the example of a charge–mass relation that can be proved within this theory and is confirmed experimentally. [ABSTRACT FROM AUTHOR]

The waveguide occupies a domain having several cylindrical outlets to infinity and is described by the non-stationary Maxwell system with perfectly conductive boundary conditions. For the corresponding stationary problem with spectral parameter, the continuous spectrum eigenfunctions and the scattering matrix are defined. We calculate the wave operators, introduce the scattering operator and describe its connection with the scattering matrix. The proof is based on extending the Maxwell system to an equation of the form with elliptic operator . We associate to the equation an initial boundary value problem and develop the scattering theory for the problem. The information on the Maxwell system is derived from the results obtained for the extended problem. [ABSTRACT FROM AUTHOR]

We build on work of Kellendonk, Richard, Tiedra de Aldecoa and others to show that the wave operators for Schrödinger scattering theory on R n generically have a particular form. As a consequence, Levinson's theorem can be interpreted as the pairing of the K -theory class of the unitary scattering operator and the K -homology class of the generator of the group of dilations. [ABSTRACT FROM AUTHOR]

This paper is devoted to solve the steady monoenergetic Fokker-Planck equation in the 1D slab when the incoming fluxes and the source term are allowed to depend on the azimuth θ. The problem is split into a collection of θ-independent problems for the Fourier coefficients of the full solution. The main difficulty is that, except for the zeroth Fourier coefficient, each of these problems contains an artificial absorption coefficient which is singular at the poles. Two numerical schemes capable of dealing with the singularities are proposed: one that is considered as the main scheme, and a second 'security' scheme which is used to verify that the results obtained by means of the first one are reliable. Numerical experiments showing second order of convergence are conducted and discussed. [ABSTRACT FROM AUTHOR]

We propose a new approach to the numerical solution of radiative transfer equations with certified a posteriori error bounds for the L2 norm. A key role is played by stable Petrov-Galerkin -type variational formulations of parametric transport equations and corresponding radiative transfer equations. This allows us to formulate an iteration in a suitable, infinite-dimensional function space that is guaranteed to converge with a fixed error reduction per step. The numerical scheme is then based on approximately realizing this iteration within dynamically updated accuracy tolerances that still ensure convergence to the exact solution. To advance this iteration two operations need to be performed within suitably tightened accuracy tolerances. First, the global scattering operator needs to be approximately applied to the current iterate within a tolerance comparable to the current accuracy level. Second, parameter dependent linear transport equations need to be solved, again at the required accuracy of the iteration. To ensure that the stage dependent error tolerances are met, one has to employ rigorous a posteriori error bounds which, in our case, rest on a Discontinuous Petrov-Galerkin (DPG) scheme. These a posteriori bounds are not only crucial for guaranteeing the convergence of the perturbed iteration but are also used to generate adapted parameter dependent spatial meshes. This turns out to significantly reduce overall computational complexity. Since the global operator is only applied, we avoid the need to solve linear systems with densely populated matrices. Moreover, the approximate application of the global scatterer is accelerated through low-rank approximation and matrix compression techniques. The theoretical findings are illustrated and complemented by numerical experiments with non-trivial scattering kernels. [ABSTRACT FROM AUTHOR]

The relativistic Lippmann–Schwinger equation was earlier formulated in terms of the limit values of the corresponding resolvent. In the present paper, we write down the limit values of the resolvent in an explicit form, and so the relativistic Lippmann–Schwinger equation is presented as an integral equation. Using this integral equation, we investigate the stationary scattering problems (relativistic case, Dirac equation). We consider the dynamical scattering problems (relativistic case, Dirac equation) as well. [ABSTRACT FROM AUTHOR]

We consider the divergences in quantum electrodynamics. Our approach is based on ideas from the theory of generalized wave operators. In particular, we use the concept of the deviation factor. The deviation factor characterizes the deviations of the initial and final waves from the free waves. The approach is demonstrated on important examples. • We present a new approach to the divergence problems, which is based on the theory of generalized wave operators. • Our approach essentially differs from the well-known Kulish-Faddeev approach. The scattering operator commutes in our case with the unperturbed operator. • The nonstationary Schrödinger and Dirac equations with Coulomb-type potentials are studied rigorously. In Dirac equation case, the results are new. • We use our deviation factor approach to interpret rigorously several important examples from the Akhiezer–Berestetskii and Pokorski books. • We show also that our approach may be used in the 4- ε dimensional case. [ABSTRACT FROM AUTHOR]

For any hypersurface M of a Riemannian manifold X , recent works introduced the notions of extrinsic conformal Laplacians and extrinsic Q -curvatures. Here we derive explicit formulas for the extrinsic version P 4 of the Paneitz operator and the corresponding extrinsic fourth-order Q -curvature Q 4 in general dimensions. In the critical dimension n = 4 , this result yields a closed formula for the global conformal invariant ∫ M Q 4 d v o l (for closed M) and various decompositions of Q 4 , which are analogs of the Alexakis/Deser-Schwimmer type decompositions of global conformal invariants. These results involve a series of obvious local conformal invariants of the embedding M 4 ↪ X 5 (defined in terms of the Weyl tensor and the trace-free second fundamental form) and a non-trivial local conformal invariant C. In turn, we identify C as a linear combination of two local conformal invariants J 1 and J 2. We also observe that these are special cases of local conformal invariants for hypersurfaces in backgrounds of general dimension. Moreover, in the critical dimension n = 4 , a linear combination of J 1 and J 2 can be expressed in terms of obvious local conformal invariants of the embedding M ↪ X. This finally reduces the non-trivial part of the structure of Q 4 to the non-trivial invariant J 1. For totally umbilic M , the invariants J i vanish, and the formula for P 4 substantially simplifies. For closed M 4 ↪ R 5 , we relate the integrals of J i to functionals of Guven and Graham-Reichert. Moreover, we establish a Deser-Schwimmer type decomposition of the Graham-Reichert functional of a hypersurface M 4 ↪ X 5 in general backgrounds. In this context, we find one further local conformal invariant J 3. Finally, we derive an explicit formula for the singular Yamabe energy of a closed M. The resulting explicit formulas show that it is proportional to the total extrinsic fourth-order Q -curvature. This observation confirms a special case of a general fact and serves as an additional cross-check of our main result. We carefully discuss the relations of our results to the recent literature, in particular to the work of Blitz, Gover and Waldron. [ABSTRACT FROM AUTHOR]

This paper considers the inverse scattering problem on the semi-axis for the matrix hyperbolic system with a special structure of matrix potential. The possible relationship between the matrix scattering operators for the first order systems with unshifted and space-shifted potentials is given. By using this relationship, the new approach for unique restoration of this potential from the matrix scattering operators on the semi-axis is given. [ABSTRACT FROM AUTHOR]

Using the example of a complicated problem such as the Cauchy problem for the Navier--Stokes equation, we show how the Poincaré--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of solutions for this case. The apparatus of the three- dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincaré--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schrödinger equation, which we consider as a velocity component in the Navier--Stokes equation. The same scheme of reduction of Riemann integral equations for the zeta function to the Poincaré--Riemann--Hilbert boundary-value problem allows us to construct effective estimates that describe the behaviour of the zeros of the zeta function very well. [ABSTRACT FROM AUTHOR]

Presents a study which examined the charging phenomenon of polymethylmethacrylate using a scanning electron microscope for the mirror image method employed. Materials and methods used; Equation expressing the scattering method; Application and discussion.

We consider the Stark operator perturbed by a compactly supported potential on the real line. We determine the forbidden domain for resonances, asymptotics of resonances at high energy and asymptotics of the resonance counting function for large radius. [ABSTRACT FROM AUTHOR]

We consider an inverse scattering problem for a non-linear Schrödinger equation with a non-linearity of power-type. Applying the time-dependent technique, developed by Enss and Weder, we prove that the non-linearity is uniquely determined from a scattering data defined via the scattering operator. We also obtain a reconstruction formula which is valid for large scattering data. [ABSTRACT FROM AUTHOR]

We consider a discrete scalar, quantum field theory based on a cubic 4-dimensional lattice. We mainly investigate a discrete scattering operator S( x , r) where x and r are positive integers representing time and maximal total energy, respectively. The operator S( x , r) is used to define transition amplitudes which are then employed to compute transition probabilities. These probabilities are conditioned on the time-energy ( x , r). In order to maintain total unit probability, the transition probabilities need to be reconditioned at each ( x , r). This is roughly analogous to renormalization in standard quantum field theory, except no infinities or singularities are involved. We illustrate this theory with a simple scattering experiment involving a common interaction Hamiltonian. We briefly mention how discreteness of spacetime might be tested astronomically. Moreover, these tests may explain the existence of dark energy and dark matter. [ABSTRACT FROM AUTHOR]

Scattering theory for Hartree equations with inverse-square potentials a|x|-2 (HE)a are considered. Recently, Suzuki [1,2] studied the global solvability and blowup in finite time for (HE)a. To observe more precise properties for global solutions, it is suitable to consider the asymptotic behavior, especially, scattering problem. [ABSTRACT FROM AUTHOR]

We prove that for the radial Schrödinger equation with Coulomb-type potential the generalized dynamical scattering operator coincides with the corresponding generalized stationary scattering operator. This fact is a quantum mechanical analogue of the ergodic results in classical mechanics. [ABSTRACT FROM AUTHOR]

In this paper, we study the global well-posedness and scattering theory of the solution to the Cauchy problem of a generalized fourth-order wave equation [ABSTRACT FROM AUTHOR]

Optically scattering phantoms composed of silica microspheres embedded in an optically clear silicone matrix were manufactured using a previously developed method. Multiple problems, such as sphere aggregation, adsorption to the cast, and silicone shrinkage, were, however, frequently encountered. Solutions to these problems were developed and an improved method, incorporating these solutions, is presented. The improved method offers excellent reliability and reproducibility for creating phantoms with uniform scattering coefficient. We also present evidence of decreased sphere aggregation. [ABSTRACT FROM AUTHOR]

We consider the nonlinear matrix Schrödinger equation on the half-line with general selfadjoint boundary condition. We prove the existence of local solutions in the corresponding energy space. Moreover, we consider the scattering problem for this problem in the scattering-supercritical regime for both generic and exceptional potentials. We construct the wave, inverse wave and scattering operators in a certain neighborhood of the origin in the scattering space Σ = H 1 ∩ L 2 , 1 for generic potentials in L 1 , 2 + η , with η > 1 / 2 , and for exceptional potentials in L 1 , 3 under further assumptions on the input data. In particular, thanks to the general boundary conditions, we are able to obtain a scattering result for the nonlinear matrix Schrödinger equation on the line with a potential and point interactions. [ABSTRACT FROM AUTHOR]

We consider the defocusing nonlinear Schrödinger equations i u +Δ u = | u| u with p being an even integer in dimensions d ≥ 5. We prove that an a priori bound of critical norm implies global well-posedness and scattering for the solution. [ABSTRACT FROM AUTHOR]

In this paper, backscattering of 3 to 50-keV positrons on Al, Cu, Ag and Au metallic targets has been systematically investigated using GEANT4 code. The dependence of positron backscattering coefficients on atomic number Z, target thickness, incident energy and angles has been discussed comprehensively. Besides, positron backscattering spectra for those metallic targets at different discrete scattering angles were also studied to provide theoretical basis of the most appropriate scattering angle selected for simulation parameters and specified applied measurement techniques. The impact of atomic number Z of targets on positron backscattering spectra was investigated as well. Simulation results are in reasonable agreement with previous experiment data and theoretical work. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The scattering operators associated to an ACHE metric of Bergman type on a strictly pseudoconvex domain are a one-parameter family of CR-conformally invariant pseudo-differential operators of Heisenberg class with respect to the induced CR structure on the boundary. In this paper, we mainly show that if the boundary Webster scalar curvature is positive, then for γ ∈ ( 0 , 1 ) the renormalised scattering operator P 2 γ has positive spectrum and satisfies the maximum principal; moreover, the fractional curvature Q 2 γ is also positive. This is parallel to the result of Guillarmou–Qing [16] for the real case. We also give two energy extension formulae for P 2 γ , which are parallel to the energy extension given by Chang–Case [2] for the real case. [ABSTRACT FROM AUTHOR]

We consider the nonlinear Dirac equation with a power nonlinearity where , . We prove the existence of the scattering operator in the neighborhood of the origin of the weighted Sobolev space , where . [ABSTRACT FROM AUTHOR]

Non-negative intensity is used to identify the surface areas of a structure that contributes to the scattered sound power. In the acoustic near field, the scattered sound power is predicted using nonnegative intensity, as well as the scattered acoustic intensity integrated directly over the scatterer's surface area. In the acoustic far field, the scattered acoustic intensity and the scattered sound power are evaluated for three different receiver surface areas, corresponding to a sphere representing a far-field area that fully circumscribes the scatterer, and two hemispherical surfaces that correspond to partial far-field areas that do not fully circumscribe the scatterer. Back-calculated non-negative intensity that defines the sound scattered from the full or partial far-field receiver surface areas is also calculated and compared to the non-negative intensity obtained directly from the surface of the scatterer. To illustrate the numerical technique, the scattered acoustic intensity and scattered sound power of a rigid sphere, a rigid cylinder, and a rigid hemispherical shell are examined. [ABSTRACT FROM AUTHOR]

Let (X , g) be a compact Riemannian manifold with boundary M n and σ a defining function of M. To these data, we associate natural conformally covariant polynomial one-parameter families of differential operators C ∞ (X) → C ∞ (M). They arise through a residue construction which generalizes an earlier construction in the framework of Poincaré-Einstein metrics and are referred to as residue families. Residue families may be viewed as curved analogs of conformal symmetry breaking differential operators. The main ingredient of the definition of residue families are eigenfunctions of the Laplacian of the singular metric σ − 2 g. We prove that if σ is an approximate solution of a singular Yamabe problem, i.e., if σ − 2 g has constant scalar curvature − n (n + 1) , up to a sufficiently small remainder, these families can be written as compositions of certain degenerate Laplacians (Laplace-Robin operators). This result implies that the notions of extrinsic conformal Laplacians and extrinsic Q -curvature introduced in recent works by Gover and Waldron can naturally be rephrased in terms of residue families. This spectral theoretical perspective allows easy new proofs of several results of Gover and Waldron. Moreover, it allows us to relate the extrinsic conformal Laplacians and the critical extrinsic Q -curvature to the scattering operator of the asymptotically hyperbolic metric σ − 2 g , extending the work of Graham and Zworski. The relation to the scattering operators implies that the extrinsic conformal Laplacians are self-adjoint. We describe the asymptotic expansion of the volume of a singular Yamabe metric in terms of Laplace-Robin operators (reproving results of Gover and Waldron). We also derive new local holographic formulas for all extrinsic Q -curvatures (critical and sub-critical ones) in terms of renormalized volume coefficients, the scalar curvature of the background metric, and the asymptotic expansions of eigenfunctions of the Laplacian of the singular metric σ − 2 g. These results naturally extend earlier results in the Poincaré-Einstein case. Furthermore, we prove a new formula for the singular Yamabe obstruction B n. The simple structure of these formulas shows the benefit of the systematic use of so-called adapted coordinates. We use the latter formula for B n to derive explicit expressions for the obstructions in low-order cases (confirming earlier results). Finally, we relate the obstruction B n to the supercritical Q -curvature Q n + 1. [ABSTRACT FROM AUTHOR]

In this paper, the inverse scattering problem for the nonstationary Dirac system on the half-plane is considered. The uniqueness criterion for the inverse scattering problem in terms of boundary condition is described and the restoration of the potential from the scattering operator is proved. [ABSTRACT FROM AUTHOR]

Several numerical experiments with the steady monoenergetic Fokker–Planck equation in the one-dimensional (1D) slab are performed and discussed. Planar-geometry symmetry is assumed. Results are obtained with a new numerical scheme of order 2 based on finite differences. [ABSTRACT FROM PUBLISHER]

We study scattering problems for the one-dimensional nonlinear Dirac equation (∂t + α∂x + iβ)Φ = λ|Φ|p−1Φ. We prove that ifp > 3 (resp.p > 3 + 1/6), then the wave operator (resp. the scattering operator) is well-defined on some 0-neighborhood of a weighted Sobolev space. In order to prove these results, we use linear operatorsD(t)xD(−t) andt∂x + x∂t − α/2, where {D(t)}t∈ℝis the free Dirac evolution group. For the reader's convenience, in an appendix we list and prove fundamental properties ofD(t)xD(−t) andt∂x + x∂t − α/2. [ABSTRACT FROM AUTHOR]

This paper is concerned with the scattering operator S for the three-dimensional Dirac equation with a cubic nonlinearity. It follows from known results that S is well-defined on a neighborhood of 0 in the Sobolev space H κ ( R 3 ; C 4 ) for any κ > 1 . In the present paper, we prove that for any M ∈ N and s ≥ max ⁡ { κ , M } , there exists some neighborhood U of 0 in the weighted Sobolev space H s , M ( R 3 ; C 4 ) such that S ( U ) ⊂ H s , M ( R 3 ; C 4 ) . [ABSTRACT FROM AUTHOR]

The scattering equations on the Riemann sphere give rise to remarkable formulas for tree-level gauge theory and gravity amplitudes. Adamo, Casali, and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the Riemann sphere that promises to have a wide application, based on off-shell scattering equations that depend on the loop momentum. We present new formulas, checked explicitly at low points, for supergravity and super-Yang-Mills amplitudes and for n-gon integrands at one loop. Finally, we show that the off-shell scattering equations naturally extend to arbitrary loop order, and we give a proposal for the all-loop integrands for supergravity and planar super-Yang-Mills theory. [ABSTRACT FROM AUTHOR]

A new integrable discretization of the nonlinear Schr¨odinger (NLS) equation is presented. Different from the one given by Ablowitz and Ladik, we discretize the time variable in this paper. The new discrete system converges to the NLS equation when we take a standard limit and has the same scattering operator as the original NLS equation. This indicates that both the new system and the NLS equation possess the same set of infinite conservation quantities. By applying the Fourier pseudo-spectral method to the space variable, we calculate the first five conservation quantities at different times. The numerical results indeed verify the conservation properties. [ABSTRACT FROM AUTHOR]

We present the design and realization of anisotropic mantle cloaks operating, at the same frequency, for both TM and TE incident polarizations. Starting from the analytical model of metasurfaces available in the literature, we first explore the potentials and limitations of the most common metasurface geometries for their application as mantle cloaks. Then, we introduce new types of patterned surfaces aimed at improving their polarization response. We demonstrate that, only by using four metasurface topologies, it is possible to obtain all required combinations of positive and negative reactance values in order to design effective mantle cloaks for planar, cylindrical, and three-dimensional (3-D) objects. We also show that the accuracy of the analytical formulas commonly used to design such metasurfaces is not necessarily sufficient for cloaking purposes. Therefore, we introduce and validate a numerical procedure to refine the analytical design and optimize the cloak performance. The effectiveness of the designed covers is checked with full-wave simulations. Finally, some antenna applications of dual-polarized mantle cloaks are proposed and several experimental measurements conducted on fabricated prototypes are also provided. [ABSTRACT FROM PUBLISHER]

Processing of large-scale scattered point clouds has currently become a hot topic in the field of computer graphics research. A supposedly valid tool in producing a set of denoised, outlier-free, and evenly distributed particles over the original point clouds, Weighted Locally Optimal Projection (WLOP) algorithm, has been used in the consolidation of unorganized 3D point clouds by many researchers. However, the algorithm is considered relatively ineffective, due to the large amount of the point clouds data and the iteration calculation. In this paper, a resampling method applied to the point set of 3D model, which significantly improves the computing speed of the WLOP algorithm. In order to measure the impact of error, which will increase with the improvement of calculation efficiency, on the accuracy of the algorithm, we define two quantitative indicators, that is, the projection error and uniformity of distribution. The performance of our method will be evaluated by using both quantitative and qualitative analyses. Our experimental validation demonstrates that this method greatly improves calculating efficiency, notwithstanding the slightly reduced projection accuracy in comparison to WLOP. [ABSTRACT FROM AUTHOR]

We review the characteristic current decomposition, first introduced by Garbacz (1968, A generalized expansion for radiated and scattered field. Ph.D. Dissertation, Ohio State University, Columbus) and then by Harrington & Mautz (1971, Theory of characteristic modes for conducting bodies. IEEE Trans. Antennas Propag., AP-19, 622–628). Our approach is based on the study of the scattering operator, or scattering matrix, the unitarity property of which plays a central role. The spectral decomposition of this operator leads to a particular characteristic far fields (or eigenfar-fields), from which a set of characteristic currents can be derived. These currents are those of Garbacz, Harrington and Mautz. They satisfy a generalized eigenequation involving usual integral operators split according to the regular/singular decomposition of the free space Green kernel. We provide proof of existence, denseness and orthogonality for these sets of characteristic modes (both currents and far fields). In addition to its theoretical interest, our analysis is motivated by its application to radar cross-section (RCS) analysis, where this particular decomposition turns out to be a powerful tool, especially for objects of small dimensions compared with the wavelength of the incident wave. Numerical computations are presented for a general three-dimensional object and the electrical field integral equation, including the first characteristic currents and their analyses in terms of their impact on the monostatic RCS. [ABSTRACT FROM AUTHOR]

In the framework of real hyperbolic geometry, this review note begins with the Helgason correspondence induced by the Poisson transform between eigenfunctions of the Laplace–Beltrami operator on the hyperbolic spaceand hyperfunctions on its boundary at infinity. Focused on the scattering operator for real hyperbolic manifolds of finite geometry, discussion is given on the two different constructions (pseudo-differential calculus for degenerate operators and harmonic analysis for the conformal group) and some applications (Selberg zeta functions, resonances and scattering poles). [ABSTRACT FROM AUTHOR]

In this paper, we show the scattering and blow up result of the solution for some coupled nonlinear Schrödinger system [ABSTRACT FROM AUTHOR]

Through-wall imaging (TWI) requires dealing with targets embedded in a complex obscuring environment such as the walls of a building. This obscuring layout is often composed by many simple elements (possibly interacting) such as slabs, corners, and T-like structures. Most of the existing literature on TWI has focused on slab-like walls, which is reasonable when the targets are relatively far from corners. This paper instead concerns the TWI in the more challenging situation where the targets are in close proximity (inside and/or outside) of a building corner. The aim is to gain insight into how propagation through the corner impacts on the imaging problem. To keep the study simple, a preliminary analysis is presented for a 2-D geometry under the linearized Born approximation. First, the Green's function, as well as the kernel of the relevant scattering operator, is evaluated by using a high-frequency analytical approach based on the geometrical optics and the uniform theory of diffraction. This allows one to take into account the multipath propagation phenomena and provide thus an expression of the scattering operator more accurate than that viable under the assumption of a simple slab wall. Then, the imaging is achieved by solving the relevant linear inverse scattering problem with a regularizing truncated-singular-value-decomposition algorithm. The filtering introduced by the inversion procedure, which is dependent on the considered background scenario, is highlighted and linked to the achievable performance while imaging targets both internal and external with respect to the corner. Finally, reconstruction results obtained from synthetic data are reported to assess the approach. [ABSTRACT FROM PUBLISHER]

We revisit the computation of the phase of the Dirac fermion scattering operator in external gauge fields. The computation is through a parallel transport along the path of time evolution operators. The novelty of the present paper compared with the earlier geometric approach by Langmann and Mickelsson (J Math Phys 37(8):3933-3953, ) is that we can avoid the somewhat arbitrary choice in the regularization of the time evolution for intermediate times using a natural choice of the connection form on the space of appropriate unitary operators. [ABSTRACT FROM AUTHOR]

Trapped modes in the linearized water wave problem are localized free oscillations in an unbounded fluid with a free surface. For sometime, it has been known that certain structures, fixed or freely floating, can support such modes. In this paper, we consider the problem on a channel, which consists of a finite part and two cylindrical outlets into infinity. The finite (bounded) part may contain some submerged and/or surface-piercing bodies. Since the ordinary scattering matrix can by no means contribute any information on trapped modes, we introduce the fictitious scattering operator and present a criterion for the existence of trapped modes. The criterion states that the number of trapped modes is the difference of the multiplicities of the eigenvalue 1 of the fictitious scattering operator and the eigenvalue − i of the scattering matrix. [ABSTRACT FROM AUTHOR]

The scattering problem for the Klein-Gordon equation with cubic convolution nonlinearity is considered. Based on the Strichartz estimates for the inhomogeneous Klein-Gordon equation, we prove the existence of the scattering operator, which improves the known results in some sense. [ABSTRACT FROM AUTHOR]

Abstract: We study spin-dependent transport in a two-dimensional waveguide with two magnetic impurities. The waveguide may have a non-trivial boundary, and the electron is coupled to the defects through contact spin–spin interactions amended by a suitable form factor to avoid divergences in the transverse-mode expansion. The scattering operator is evaluated in a fully multi-channel framework, and entanglement production analyzed by studying both the transmission coefficients, and the concurrence between the defects' spin degrees of freedom. For non-entangled incoming states, entanglement production is enhanced in correspondence to resonance transmission. Differently from one-dimensional, single-channel scattering, however, no tendency toward robust entanglement production is observed with increasing energy. On the other hand, the peculiar role played by the maximally entangled singlet state of the impurities in electron transmission is confirmed in these multi-channel calculations. In this case also, the whole scenario is significantly more complex than in strictly one-dimensional systems, because of the opening of thresholds with increasing energy, and the presence of evanescent modes, whose effects cannot be ignored. [Copyright &y& Elsevier]