Related papers: Factorization for the matrix-valued general Jacobi…
We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the…
We develop direct and inverse scattering theory for Jacobi operators with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give a complete characterization of…
We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing of the scattering…
We consider scattering theory for one-dimensional Jacobi operators with respect to steplike quasi-periodic finite-gap backgrounds and show how the transmission coefficient can be reconstructed from minimal scattering data. This generalizes…
We present a new exact algorithm for estimating all elements of the quark propagator. The advantage of the method is that the exact all-to-all propagator is reproduced in a large but finite number of inversions. The efficacy of the…
Transfer matrix method is a well-known and extensively used tool to compute the reflection and transmission coefficients of electromagnetic waves when interacting with a system of layers parallel to each other. We present here a modified…
We present a direct and simple method for the computation of the total scattering matrix of an arbitrary finite noncompact connected quantum graph given its metric structure and local scattering data at each vertex. The method is inspired…
In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…
The scattering matrix, which quantifies the optical reflection and transmission of a photonic structure, is pivotal for understanding the performance of the structure. In many photonic design tasks, it is also desired to know how the…
We initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in partitioning the poset of factorization systems on a fixed…
We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal…
A semi-infinite crack in infinite square lattice is subjected to a wave coming from infinity, thereby leading to its scattering by the crack surfaces. A partially damaged zone ahead of the crack-tip is modeled by an arbitrarily distributed…
We show that every tropical totally positive matrix can be uniquely represented as the transfer matrix of a canonical totally connected weighted planar network. We deduce a uniqueness theorem for the factorization of a tropical totally…
Left-modularity is a concept that generalizes modularity in lattice theory. In this paper, we give a characterization of left-modular elements and derive two formulae for the characteristic polynomial of a lattice with such an element, one…
We consider the lattice of all the weak factorization systems on a given finite lattice. We prove that it is semidistributive, trim and congruence uniform. We deduce a graph theoretical approach to the problem of enumerating transfer…
A novel efficient method to calculate the scattering matrix (SM) of arbitrary tight-binding Hamiltonians is proposed, including cases with multiterminal structures. In particular, the SM of two kind of fundamental structures are given,…
It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor…
In this text we generalize the classical Jacobi Eisenstein series as they were discussed by Eichler and Zagier to arbitrary lattices. We use two different methods to derive the general Fourier expansion. The last two sections give formulas…
We study Taylor expansions of Jacobi forms of lattice index. As the main result, we give an embedding from certain space of such forms, whether scalar-valued or vector-valued, integral-weight or half-integral-weight, of any level, with any…
We investigate numerically different techniques to extract scattering amplitudes from the Euclidean Lattice {\phi}4 theory with two fields, having different masses. We present an exploratory study of the recently proposed method by Bruno…