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In recent years a considerable amount of attention has been devoted to the investigation of 2D quantum field theories perturbed by certain types of irrelevant operators. These are the composite field T T ― —constructed out of the components of the stress-energy tensor—and its generalisations—built from higher-spin conserved currents. The effect of such perturbations on the infrared and ultraviolet properties of the theory has been extensively investigated. In the context of integrable quantum field theories, a fruitful perspective is that of factorised scattering theory. In fact, the above perturbations were shown to preserve integrability. The resulting deformed scattering matrices—extensively analysed with the thermodynamic Bethe ansatz—provide the first step in the development of a bootstrap program. In this paper we present a systematic approach to computing matrix elements of operators in generalised T T ― -perturbed models, based on employing the standard form factor program. We show that for theories with diagonal scattering and certain types of fields the deformed form factors, factorise into the product of the undeformed ones and of a perturbation- and theory-dependent term. From these solutions, correlation functions can be obtained and their asymptotic properties studied. [ABSTRACT FROM AUTHOR]

Recent advances in electron microscopy allowed the generation of high-energy electron wave packets of ultrashort duration. Here we present a non-perturbative S -matrix theory for scattering of ultrashort electron wave packets by atomic targets. We apply the formalism to a case of elastic scattering and derive a generalized optical theorem for ultrashort wave-packet scattering. By numerical simulations with 1 fs wave packets, we find in angular distributions of electrons on a detector one-fold and anomalous two-fold azimuthal asymmetries. We discuss how the asymmetries relate to the coherence properties of the electron beam, and to the magnitude and phase of the scattering amplitude. The essential role of the phase of the exact scattering amplitude is revealed by comparison with results obtained using the first-Born approximation. Our work paves a way for controlling electron-matter interaction by the lateral and transversal coherence properties of pulsed electron beams.

Evanescent waves are waves that decay or grow exponentially in regions of the space void of interaction. In potential scattering defined by the Schrödinger equation, (âˆ' ∇ 2 + v) ψ = k 2 ψ for a local potential v, they arise in dimensions greater than one and are generally present regardless of the details of v. The approximation in which one ignores the contributions of the evanescent waves to the scattering process corresponds to replacing v with a certain energy-dependent nonlocal potential V k ˆ . We present a dynamical formulation of the stationary scattering for V ˆ k in two dimensions, where the scattering data are related to the dynamics of a quantum system having a non-self-adjoint, unbounded, and nonstationary Hamiltonian operator. The evolution operator for this system determines a two-dimensional analog of the transfer matrix of stationary scattering in one dimension which contains the information about the scattering properties of the potential. Under rather general conditions on v, we establish the strong convergence of the Dyson series expansion of the evolution operator and prove the existence of the transfer matrix for V ˆ k as a densely-defined operator acting in C 2 ⊗ L 2 (âˆ' k , k). [ABSTRACT FROM AUTHOR]

The scattering matrices of e + N+ with JĎ€ = 1.5+ in discrete energy regions are calculated using the eigenchannel R-matrix method. We obtain good parameters of multichannel quantum defect theory (MQDT) that vary smoothly as the function of the energy resulting from the analytical continuation property of the scattering matrices. By employing the MQDT, all discrete energy levels for N could be calculated accurately without missing anyone. The MQDT parameters (i.e., scattering matrices) can be calibrated with the available precise spectroscopy values. In this work, the optical oscillator strengths for the transition between the ground state and Rydberg series are obtained, which provide rich data for the diagnostic analysis of plasma. [ABSTRACT FROM AUTHOR]

A spectral shift function (SSF) is an important object in the scattering theory which is related both to the spectral density and to the scattering matrix. In the paper, it is shown how to employ the SSF formalism to solve scattering problems when the continuum is discretized, e.g. when solving a scattering problem in a finite volume or in the representation of some finite square-integrable basis. A new algorithm is proposed for reconstructing integrated densities of states and the SSF using a union of discretized spectra corresponding to a set of Gaussian bases with the shifted scale parameters. The examples given show that knowledge of the discretized spectra of the total and asymptotic Hamiltonians is sufficient to find the scattering partial phase shifts at any required energy, as well as the resonances parameters. [ABSTRACT FROM AUTHOR]

The energies and wavefunctions of both localized and resonant states are calculated for Coulomb acceptor in narrow-gap HgCdTe alloys with cadmium mole fraction from 0% to 30%. The simulation is performed with scattering matrix method within a spherically-symmetric three-band Kane model that takes into account the conduction band and two valence bands. The energies of both localized and resonant states are determined using the localization rate magnitude, introduced in this work. [ABSTRACT FROM AUTHOR]

All currently known exactly solvable multistate Landau–Zener (MLZ) models are associated with families of operators that commute with the MLZ Hamiltonians and depend on time linearly. There can also be operators that satisfy the integrability conditions with the MLZ Hamiltonians but depend on time quadratically. We show that, among the MLZ systems, such time-quadratic operators are much more common. We demonstrate then that such operators generally lead to constraints on the independent variables that parametrize the scattering matrix. Such constraints lead to asymptotically exact expressions for the transition probabilities in the adiabatic limit of a three-level MLZ model. New more complex fully solvable MLZ systems are also found. [ABSTRACT FROM AUTHOR]

We use the Baranger model to compute collisional broadening and shift rates for the D1 and D2 spectral lines of M + Ng, where M = K, Rb, Cs and Ng = He, Ne, Ar. Scattering matrix elements are calculated using the channel packet method, and non-adiabatic wavepacket dynamics are determined using the split-operator method together with a unitary transformation between adiabatic and diabatic representations. Scattering phase shift differences are weighted thermally and are integrated over temperatures ranging from 100 K to 800 K. We find that predicted broadening rates compare well with experiment, but shift rates are predicted poorly by this model because they are extremely sensitive to the near-asymptotic behavior of the potential energy surfaces. [ABSTRACT FROM AUTHOR]

We consider a multichannel wire with a disordered region of length L and a reflecting boundary. The reflection of a wave of frequency ω is described by the scattering matrix , encoding the probability amplitudes to be scattered from one channel to another. The Wigner–Smith time delay matrix is another important matrix, which encodes temporal aspects of the scattering process. In order to study its statistical properties, we split the scattering matrix in terms of two unitary matrices, (with in the presence of time reversal symmetry), and introduce a novel symmetrisation procedure for the Wigner–Smith matrix: , where k is the wave vector and v the group velocity. We demonstrate that can be expressed under the form of an exponential functional of a matrix Brownian motion. For semi-infinite wires, L → ∞, using a matricial extension of the Dufresne identity, we recover straightforwardly the joint distribution for 's eigenvalues of Brouwer and Beenakker (2001 Physica E 9 463). For finite length L, the exponential functional representation is used to calculate the first moments , and. Finally we derive a partial differential equation for the resolvent in the large N limit. [ABSTRACT FROM AUTHOR]

We discuss solvable multistate Landau–Zener (MLZ) models whose Hamiltonians have commuting partner operators with ∼1/τ-time-dependent parameters. Many already known solvable MLZ models belong precisely to this class. We derive the integrability conditions on the parameters of such commuting operators, and demonstrate how to use such conditions in order to derive new solvable cases. We show that MLZ models from this class must contain bands of parallel diabatic energy levels. The structure of the scattering matrix and other properties are found to be the same as in the previously discussed completely solvable MLZ Hamiltonians. [ABSTRACT FROM AUTHOR]

Considering, as a limit case, an approximately flat pion distribution amplitude, which is determined from the hardest, in momentum space, solution of the Bethe–Salpeter equation for the pion wave function, we compute the pion transition form factor and the pion form factor Fπ(Q2), taking into account the LO as well as NLO form of the hard coefficient function entering the leading-twist factorization formula. We also compute the exclusive photoproduction of pions pairs at high energies, , where perturbative QCD can be used to compute the hard scattering matrix elements. We verify that the existent data for exclusive pion production can be reasonably described as a function of such a flat distribution amplitude. [ABSTRACT FROM AUTHOR]

In this study, we compute cross sections for vibrational excitation of NO2 by electron impact. Calculations are performed using a theoretical approach based on a combination of the normal mode approximation for vibrational states of the target molecule, fixed-nuclei electron-NO2 scattering matrices and the vibrational frame transformation employed to evaluate the scattering matrix for vibrational transitions. Thermally-averaged rate coefficients are derived from the obtained cross sections for temperatures in the 10–10000 K interval for excitation of each normal mode of the target molecule. Analytical fits for the rate coefficients for singlets and triplets are provided. In addition, a comprehensive set of calculations are performed for assessing the uncertainty of the present calculations. The uncertainty assessments indicate that the computed observables for vibrational (de-)excitation is reasonable for later use in NO2-containing plasma kinetics modeling. [ABSTRACT FROM AUTHOR]

In this study, we compute cross sections for vibrational excitation of NO2 by electron impact. Calculations are performed using a theoretical approach based on a combination of the normal mode approximation for vibrational states of the target molecule, fixed-nuclei electron-NO2 scattering matrices and the vibrational frame transformation employed to evaluate the scattering matrix for vibrational transitions. Thermally-averaged rate coefficients are derived from the obtained cross sections for temperatures in the 10–10000 K interval for excitation of each normal mode of the target molecule. Analytical fits for the rate coefficients for singlets and triplets are provided. In addition, a comprehensive set of calculations are performed for assessing the uncertainty of the present calculations. The uncertainty assessments indicate that the computed observables for vibrational (de-)excitation is reasonable for later use in NO2-containing plasma kinetics modeling. [ABSTRACT FROM AUTHOR]

We report on the experimental investigation of the properties of the eigenvalues and wavefunctions and the fluctuation properties of the scattering matrix of closed and open billiards, respectively, of which the classical dynamics undergoes a transition from integrable via almost integrable to fully chaotic. To realize such a system, we chose a billiard with a 60° sector shape of which the classical dynamics is integrable, and introduced circular scatterers of varying number, size, and position. The spectral properties of generic quantum systems of which the classical counterpart is either integrable or chaotic are universal and well understood. If, however, the classical dynamics is pseudo-integrable or almost-integrable, they exhibit a non-universal intermediate statistics, for which analytical results are known only in a few cases, e.g., if it corresponds to semi-Poisson statistics. Since the latter is, above all, clearly distinguishable from those of integrable and chaotic systems, our aim was to design a billiard with these features which indeed is achievable by adding just one scatterer of appropriate size and position to the sector billiard. We demonstrated that, while the spectral properties of almost-integrable billiards are sensitive to the classical dynamics, this is not the case for the distribution of the wavefunction components, which was analyzed in terms of the strength distribution, and the fluctuation properties of the scattering matrix which coincide with those of typical, fully chaotic systems. [ABSTRACT FROM AUTHOR]

We study form factors in the light-cone gauge world-sheet theory for strings in AdS5 ×S5. We perturbatively calculate the two-particle form factor in a closed sector to one-loop in the near-plane-wave limit and to two-loops in the Maldacena–Swanson limit. We also perturbatively solve the functional equation which follows from the form factor axioms for the world-sheet theory and show that the ‘minimal’ solution correctly reproduces the discontinuities of the perturbative calculations. Finally we propose a prescription, valid for polynomial orders of the inverse world-sheet length, for extracting the finite-volume world-sheet matrix element from the form factors and show that the two-excitation matrix element matches with the thermodynamic limit of the spin–chain description of certain tree-level SYM structure constants. [ABSTRACT FROM AUTHOR]

Here, we address the question of the validity of an effective description for hyperbolic metamaterials in the near-field region. We show that the presence of localized modes such as surface waves drastically limits the validity of the effective description, and requires revisiting the concept of homogenization in the near-field. We demonstrate, from exact scattering matrix calculations for multilayer hyperbolic structures, that one can find surface modes in spectral regions where the effective approach predicts hyperbolic modes only. Hence, the presence of surface modes which are not accounted for in the effective description can lead to physical misinterpretations in the description of hyperbolic materials and their related properties. In particular, we discuss in detail how the choice of the topmost layer affects the validity of the effective medium approach for calculating the local density of states and the super-Planckian thermal radiation. [ABSTRACT FROM AUTHOR]

We investigate the limit properties of a family of Schrödinger operators of the form Hϵ = -d2/dx2 + λ(ϵ)/ϵ2 Q (x/ϵ) acting on n-edge star graphs with the Kirchhoff interface conditions at the vertex. Here the real-valued potential Q has compact support and λ(∙) is analytic around ϵ = 0 with λ(0) = 1. We show that if the operator has a zero-energy resonance of order m for ϵ = 1 and λ(1) = 1, in the limit ϵ → 0 one obtains the Laplacian with a vertex coupling depending on 1+ 1/2 m(2n-m+1) parameters. We prove the norm-resolvent convergence as well as the convergence of the corresponding on-shell scattering matrices. The obtained vertex couplings are of scale-invariant type provided λ' (0) = 0; otherwise the scattering matrix depends on energy and the scaled potential becomes asymptotically opaque in the low-energy limit. [ABSTRACT FROM AUTHOR]

We construct a perturbative S-matrix for interacting massive scalar fields in global de Sitter space. Our S-matrix is formulated in terms of asymptotic particle states in the far past and future, taking appropriate care for light fields whose wavefunctions decay only very slowly near the de Sitter conformal boundaries. An alternative formulation expresses this S-matrix in terms of residues of poles in analytically-continued Euclidean correlators (computed in perturbation theory), making it clear that the standard Minkowski-space result is obtained in the flat-space limit. Our S-matrix transforms properly under CPT, is invariant under the de Sitter isometries and perturbative field redefinitions, and is unitary. This unitarity implies a de Sitter version of the optical theorem. We explicitly verify these properties to second order in the coupling for a general cubic interaction, including both tree- and loop-level contributions. Contrary to other statements in the literature, we find that a particle of any positive mass may decay at tree level to any number of particles, each of arbitrary positive masses. In particular, even very light fields (in the complementary series of de Sitter representations) are not protected from tree-level decays. [ABSTRACT FROM AUTHOR]

In recent times, coherent Fourier scatterometry has been considered as an emerging optical grating scatterometry technique for semiconductor metrology since it shows large sensitivity owing to its scanning ability. However, further utilization of coherence is possible by making additional measurements using the principle of temporal phase-shifting interferometry. In this paper, through numerical simulation, we show how scanning and interferometry can be coupled together to improve the sensitivity of coherent Fourier scatterometry, to extend its range of applicability and to obtain sufficient information to calculate the complex scattering matrix for all angles of incidences inside the numerical aperture of a microscope objective. [ABSTRACT FROM AUTHOR]

We show that, in the context of the R-matrix method, the eigenvalues of the Hamiltonian matrix in a finite basis spanning the inner configuration space can be used to generate a set of accurate values of the S-matrix at these eigenenergies. This set is then used as input in an analytic continuation scheme to locate several resonances accurately in the complex energy plane. [ABSTRACT FROM AUTHOR]

We study the constraints imposed by the existence of a single higher spin conserved current on a three-dimensional conformal field theory (CFT). A single higher spin conserved current implies the existence of an infinite number of higher spin conserved currents. The correlation functions of the stress tensor and the conserved currents are then shown to be equal to those of a free field theory. Namely a theory of N free bosons or free fermions. This is an extension of the Coleman-Mandula theorem to CFT's, which do not have a conventional S-matrix. We also briefly discuss the case where the higher spin symmetries are 'slightly' broken. [ABSTRACT FROM AUTHOR]

We reviewsome recentwork on AdS/CFT duality involving the 3D O(N) vector model and AdS4 higher spin gravity. Our construction is based on bi-local collective field theory which provides an off-shell formulation of higher spin gravity with G = 1/N playing the role of a coupling constant. Consequently, perturbative and non-perturbative issues of the theory can be studied. For the correspondence based on free CFTs we discuss the nature of bulk 1/N interactions through an S-matrix which is argued to be equal to 1 (Coleman- Mandula theorem). As a consequence in this class of theories nonlinearities are removable, through a nonlinear field transformation which we show at the exact level.We also describe a geometric (Kähler space) framework for the bilocal theory which applies equally simply to Sp(2N) fermions and the de Sitter correspondence. We discuss in this framework the structure and size of the bi-local Hilbert space and the implementation of (finite N) exclusion principle. [ABSTRACT FROM AUTHOR]

This review is devoted to the intriguing and still largely unexplored links between string theory and higher spins, the types of excitations that lie behind their most cherished properties. A closer look at higher spin fields provides some further clues that string theory describes a broken phase of a higher spin gauge theory. Conversely, string amplitudes contain a wealth of information on higher spin interactions that can clarify long-standing issues related to their infrared behavior. [ABSTRACT FROM AUTHOR]

We generalize eigenphase-preserving (EPP) supersymmetric (SUSY) transformations to an N >2 channel Schrödinger equation with equal thresholds. It is established that EPP SUSY transformations exist only in the case of an even number of channels, N = 2M. A single EPP SUSY transformation provides an M(M-1)+2 parametric deformation of the matrix Hamiltonian without affecting eigenphase shifts of the scattering matrix. [ABSTRACT FROM AUTHOR]

We consider a thought experiment in which an energetic massless string probes a 'stringhole' (a heavy string lying on the correspondence curve between strings and black holes) at large enough impact parameter for the regime to be under theoretical control. The corresponding, explicitly unitary, S-matrix turns out to be perturbatively sensitive to the microstate of the stringhole: in particular, at leading order in ls/b, it depends on a projection of the stringhole's Lorentz-contracted quadrupolemoment. The string-black hole correspondence is therefore violated if one assumes quantum hair to be exponentially suppressed as a function of black-hole entropy. Implications for the information paradox are briefly discussed. [ABSTRACT FROM AUTHOR]

This paper presents an analytic inversion method for a polarimetric synthetic-aperture radar (SAR) in the case of an extended target embedded in clutter. The measurements are also contaminated by thermal noise. We use microlocal analysis in a statistical setting to develop a filtered-backprojection-type reconstruction method. The inversion method accommodates arbitrary waveforms and arbitrary flight paths. We model the antennas and scatterers as dipoles; scatterers are thus characterized by a spatially varying scattering matrix. We include directional scattering assumptions to distinguish a curve-like extended target from clutter, which is assumed to scatter isotropically. For the inversion we choose the backprojection filter which minimizes the mean-square error between the reconstructed image and the actual target scattering matrix. Our work differs from standard polarimetric SAR imaging in that we do not perform channel-by-channel image reconstruction. We find that it is preferable to use a coupled reconstruction scheme in which we use all sets of collected data to form each element of the scattering matrix. We show in our numerical experiments that the coupled reconstruction not only minimizes the mean-square error but also improves the image target-to-clutter ratio in certain scenarios. [ABSTRACT FROM AUTHOR]

Nonsequential double ionization (NSDI) processes of nonaligned diatomic molecules N2 and O2 are studied using the S-matrix theory. Our results show that the NSDI process significantly depends on the molecular symmetry and structure. The ratio of NSDI rate to single ionization rate as a function of the field intensity is obtained. It is found that N2 behaves closely with its companion atom Ar in the ratios over the entire intensity range, while O2 exhibits an obvious suppression effect, which is qualitatively consistent with the experiment. [ABSTRACT FROM AUTHOR]

Nonsequential double ionization (NSDI) processes of nonaligned diatomic molecules N2 and O2 are studied using the S-matrix theory. Our results show that the NSDI process significantly depends on the molecular symmetry and structure. The ratio of NSDI rate to single ionization rate as a function of the field intensity is obtained. It is found that N2 behaves closely with its companion atom Ar in the ratios over the entire intensity range, while O2 exhibits an obvious suppression effect, which is qualitatively consistent with the experiment. [ABSTRACT FROM AUTHOR]

The impact approximation used in the modelling of Stark profiles is examined when a magnetic field is present. Motivated by tokamak plasma spectroscopy, we calculate line shapes and S-matrix elements for the first Lyman lines of hydrogen with two models proposed for retaining simultaneously Stark and Zeeman effects in the impact limit. An evaluation of the accuracy of the two approaches is made with the help of a numerical simulation. [ABSTRACT FROM AUTHOR]

We find a new quantum affine symmetry of the S-matrix of the one-dimensional Hubbard chain. We show that this symmetry originates from the quantum affine superalgebra Uq(gl(2|2)), and in the rational limit exactly reproduces the secret symmetry of the AdS/CFT worldsheet S-matrix. [ABSTRACT FROM AUTHOR]

For a two-dimensional quantum-mechanical problem, we obtain a generalized power series expansion of the S-matrix that can be done near an arbitrary point on the Riemann surface of the energy, similar to the standard effective-range expansion. In order to do this, we consider the Jost function and analytically factorize its momentum dependence that causes the Jost function to be a multivalued function. The remaining single-valued function of the energy is then expanded in the power series near an arbitrary point in the complex energy plane. A systematic and accurate procedure has been developed for calculating the expansion coefficients. This makes it possible to obtain a semi-analytic expression for the Jost function (and therefore for the S-matrix) near an arbitrary point on the Riemann surface and use it, for example, to locate the spectral points (bound and resonant states) as the S-matrix poles. The method is applied to a model similar to those used in the theory of quantum dots. [ABSTRACT FROM AUTHOR]

We study topological phase transitions in discrete gauge theories in two spatial dimensions induced by the formation of a Bose condensate. We analyse a general class of euclidean lattice actions for these theories which contain one coupling constant for each conjugacy class of the gauge group. To probe the phase structure we use a complete set of open and closed anyonic string operators. The open strings allow one to determine the particle content of the condensate, whereas the closed strings enable us to determine the matrix elements of the modular S-matrix, in both the unbroken and broken phases. From the measured broken S-matrix we may read off the sectors that split or get identified in the broken phase, as well as the sectors that are confined. In this sense the modular S-matrix can be employed as a matrix valued nonlocal order parameter from which the low-energy effective theories that occur in different regions of parameter space can be fully determined. To verify our predictions, we studied a non-abelian anyon model based on the quaternion group H = …2 of the order of eight by Monte Carlo simulation. We probe part of the phase diagram for the pure gauge theory and find a variety of phases with magnetic condensates leading to various forms of (partial) confinement in complete agreement with the algebraic breaking analysis. Also the order of various transitions is established. [ABSTRACT FROM AUTHOR]

Using the scattering-matrix method, we investigate the thermal conductance in a two-slit quantum waveguide at low temperature. The results show that the total thermal conductance decreases monotonically with temperature increasing. Moreover, we find that the behaviours of the thermal conductance versus temperature are different for different types of slits. [ABSTRACT FROM AUTHOR]

In this paper, we present the numerical results of conduction in a disordered quasi-one-dimensional wire in the possible presence of magnetic impurities. Our analysis leads us to the study of universal properties in different conduction regimes, such as the localized and metallic ones. In particular, we analyze the crossover between universality classes occurring when the strength of magnetic disorder is increased. For this purpose, we use a numerical Landauer approach, and derive the scattering matrix of the wire from the electron's Green's function. [ABSTRACT FROM AUTHOR]

We describe a new formalism to fit the parameters α and β that are used in the SALT2 model to determine the standard magnitudes of Type la supernovae (SNe Ia). The new formalism describes the intrinsic scatter in SNe Ia by a covariance matrix in place of the single parameter normally used. We have applied this formalism to the Sloan Digital Sky Survey Supernova Survey (SDSS-II) data and conclude that the data are best described by α = Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. and β = Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., where the error is dominated by the uncertainty in the form of the intrinsic scatter matrix. Our result depends on the introduction of a more general form for the intrinsic scatter of the distance moduli of SNe la than is conventional, resulting in a larger value of β and a larger uncertainty than the conventional approach. Although this analysis results in a larger value of β and a larger error, the SDSS data differ (at a 98% confidence level) from β -- 4.1, the value expected for extinction by the type of dust found in the Milky Way. We have modeled the distribution of SNe Ia in terms of their color and conclude that there is strong evidence that variation in color is a significant contributor to the scatter of SNe la around their standard candle magnitude. [ABSTRACT FROM AUTHOR]

The photoelectron angular distributions (PADs) of hydrogen atoms in an intense laser field of linear polarization are studied using the S-matrix theory in the length gauge. The PADs show main lobes along the laser polarization and jet-like structures sticking from the waist of main lobes. Our previous prediction, based on a nonperturbative scattering theory of photoionization developed by Guo et al, showing that the number of jets on one side of PADs may increase by one, three, or other odd numbers and may decrease by one when one more photon is absorbed, is confirmed by this treatment. Within the strong-field approximation, good agreement is obtained between these two quite different treatments. We further study the influence of the Coulomb attraction to PADs, by taking a Coulomb-Volkov state as the continuum state of photoelectrons. We find that under the influence of the Coulomb attraction, the PADs change greatly but the predicted phenomena still appear. This study verifies that the jet-like structures have no relation with the angular momentum of photoelectrons. [ABSTRACT FROM AUTHOR]

This paper considers the frequency-quadrupling three-cavity gyroklystrons with successive frequency-doubling in each cavity. The cavities of 225 GHz frequency-quadrupling gyroklystron are designed with the scattering matrices method and the possible operating mode are discussed. With the point-gap theory, the starting currents of the possible operating modes and the potential parasitic modes in the output cavity are calculated. The optimal operating mode is proposed under consideration of the mode competition and the power capacity of the cavity. [ABSTRACT FROM AUTHOR]

In this paper, a new type of resonant Brewster filters (RBF) with surface relief structure for the multiple channels is first presented by using the rigorous coupled-wave analysis and the S-matrix method. By tuning the depth of homogeneous layer which is under the surface relief structure, the multiple channels phenomenon is obtained. Long range, extremely low sidebands and multiple channels are found when the RBF with surface relief structure is illuminated with Transverse Magnetic incident polarization light near the Brewster angle calculated with the effective media theory of sub wavelength grating. Moreover, the wavelengths of RBF with surface relief structure can be easily shifted by changing the depth of homogeneous layer while its optical properties such as low sideband reflection and narrow band are not spoiled when the depth is changed. Furthermore, the variation of the grating thickness does not effectively change the resonant wavelength of RBF, but have a remarkable effect on its line width, which is very useful for designing such filters with different line widths at desired wavelength. [ABSTRACT FROM AUTHOR]

It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the S-matrix along the real positive energy axis. No calculations of the S-matrix at complex energies or a complex rotation are necessary. The proposed method is therefore universal in that it is applicable to any potential (local, non-local, discontinuous, etc) provided that there is a way of obtaining the S-matrix (or scattering phase shifts) at real collision energies. Besides this, combined with any method that extracts the phase shifts from the scattering data, the proposed rational parametrization technique would be able to do the spectral analysis using the experimental data. [ABSTRACT FROM AUTHOR]

We use the coordinate Bethe ansatz approach to derive the nested Bethe equations corresponding to the recently found S-matrix for strings in AdS5 × S5, compatible with centrally extended \mathfrak{su}(2|2) symmetry. [ABSTRACT FROM AUTHOR]

We describe a new class of scattering matrices for quantum graphs in which back-scattering is prohibited. We discuss some properties of quantum graphs with these scattering matrices and explain the advantages and interest in their study. We also provide two methods to build the vertex scattering matrices needed for their construction. [ABSTRACT FROM AUTHOR]

In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher order differential operators as an intermediary. In this paper, the case of quantum graphs is addressed. A quantum graph is a graph considered as a (singular) one-dimensional variety and equipped with a second-order differential Hamiltonian H (a 'Laplacian') with suitable conditions at vertices. For the case of scale-invariant vertex conditions (i.e. conditions that do not mix the values of functions and of their derivatives), the constant term of the heat-kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph. This observation is placed into the index-theory context by factoring the Laplacian into two first-order operators, H = A*A, and relating the constant term to the index of A. An independent consideration provides an index formula for any differential operator on a finite quantum graph in terms of the vertex conditions. It is also found that the algebraic multiplicity of 0 as a root of the secular determinant of H is the sum of the nullities of A and A*. [ABSTRACT FROM AUTHOR]

We consider a superconductor/multiferromagnet/superconductor (S/I/F1/[?] [?] [?]/Fn/I/S) ballistic junction with thin insulating layers in the interfaces. We develop a diagrammatic approach for the equation that determines the Andreev spectrum, by examining the closed loops in the intermediate ferromagnetic layers. It is expressed in terms of the S/F and F/F interface scattering amplitudes. A set of rules is determined. Several analytical formulas are obtained, and in particular we study the triple ferromagnetic layer case. We also obtain the maximum current from the scattering matrix, and show that it is consistent with the diagrammatic approach. A specific application is the asymmetric S/F/I/S junction. The diagrammatic approach is also checked with the matrix of scattering amplitudes method. [ABSTRACT FROM AUTHOR]

We show how to construct discrete-time quantum walks on directed, Eulerian graphs. These graphs have tails on which the particle making the walk propagates freely, and this makes it possible to analyze the walks in terms of scattering theory. The probability of entering a graph from one tail and leaving from another can be found from the scattering matrix of the graph. We show how the scattering matrix of a graph that is an automorphic image of the original is related to the scattering matrix of the original graph, and we show how the scattering matrix of the reverse graph is related to that of the original graph. Modifications of graphs and the effects of these modifications are then considered. In particular we show how the scattering matrix of a graph is changed if we remove two tails and replace them with an edge or cut an edge and add two tails. This allows us to combine graphs, that is if we connect two graphs we can construct the scattering matrix of the combined graph from those of its parts. Finally, using these techniques, we show how two graphs can be compared by constructing a larger graph in which the two original graphs are in parallel, and performing a quantum walk on the larger graph. This is a kind of quantum walk interferometry. [ABSTRACT FROM AUTHOR]

In the present work, a general frame for the scattering theory of local, relativistic dipole quantum fields is presented and some models of interacting dipole fields are considered, i.e. local, relativistic quantum fields with an indefinite metric which asymptotically do not converge to free fields, but to free dipole fields. Also, we give explicit formulae for the (nontrivial) scattering matrix of dipole in- and out-fields for these models. Furthermore, we show how the related dipole degrees of freedom occur in the perturbation theory of certain two-dimensional models, e.g. massive sine-Gordon or sinh-Gordon models. [ABSTRACT FROM AUTHOR]

The right-hand boundary of Artin's billiard on the Poincaré half-plane is continuously deformed to generate a class of chaotic billiards which includes fundamental domains of the Hecke groups ?(2, n) at certain values of the deformation parameter. The quantum scattering problem in these open chaotic billiards is described and the distributions of both real and imaginary parts of the resonant eigenvalues are investigated. The transitions to arithmetic chaos in the cases n? {4, 6} are closely examined and the explicit analytic form for the scattering matrix is given together with the Fourier coefficients for the scattered wavefunction. The n= 4 and 6 cases have an additional set of regular equally spaced resonances compared to Artin's billiard (n= 3). For a general deformation, a numerical procedure is presented which generates the resonance eigenvalues and the evolution of the eigenvalues is followed as the boundary is varied continuously which leads to dramatic changes in their distribution. For deformations away from the non-generic arithmetic cases, including that of the tiling Hecke triangular billiard n= 5, the distributions of the positions and widths of the resonances are consistent with the predictions of a random matrix theory. [ABSTRACT FROM AUTHOR]

It was recently noted that the dispersion relation for the magnons of planar SYM can be identified with the Casimir of a certain deformation of the Poincaré algebra, in which the energy and momentum operators are supplemented by a boost generator J. By considering the relationship between Jand , we derive a q-deformed super-Poincaré symmetry algebra of the kinematics. Using this, we show that the dynamic magnon representations may be obtained by boosting from a fixed rest-frame representation. We comment on aspects of the coalgebra structure and some implications for the question of boost covariance of the S-matrix. [ABSTRACT FROM AUTHOR]

Layer stripping based on the Riccati equation for the scattering matrix is a natural approach to the solution of the inverse scattering problem for the Helmholtz equation. But it has so far failed to work in two and three dimensions. This paper examines a cause of failure and establishes a Riccati equation for the scattering matrix on the level surfaces of the index of refraction. The new Riccati equation overcomes a common drawback shared by the traditional Riccati equations—the waves are unnaturally forced to propagate with a Green's function of an artificially fixed background wave number, and this man-made mismatch will mix and deform the propagating and evanescent modes, which skews the regularization of the backward solve of the Riccati equations for layer stripping. [ABSTRACT FROM AUTHOR]

Using the scattering-matrix method, we investigate the acoustic phonon ballistic transmission and thermal conductivity in a dielectric quantum wire structure. We find that the transmission coefficient and the thermal conductivity are of quantum character, and sensitively depend on the geometric parameters and material nature of the structure. The transmission coefficient of the single acoustic phonon mode with differing frequency has different dependence on geometric configurations. Our results show that by adjusting the structural parameters and material nature one can control the thermal conductivity of the structure to match practical requirements in devices. [ABSTRACT FROM AUTHOR]