Related papers: The transfer matrix: a geometrical perspective
We reelaborate on the basic properties of lossless multilayers. We show that the transfer matrices for these multilayers have essentially the same algebraic properties as the Lorentz group SO(2,1) in a (2+1)-dimensional spacetime, as well…
We elaborate on the consequences of the factorization of the transfer matrix of any lossless multilayer in terms of three basic matrices of simple interpretation. By considering the bilinear transformation that this transfer matrix induces…
We present a self-contained discussion of the use of the transfer-matrix formalism to study one-dimensional scattering. We elaborate on the geometrical interpretation of this transfer matrix as a conformal mapping on the unit disk. By…
We reconsider the quantum inverse scattering approach to the one-dimensional Hubbard model and work out some of its basic features so far omitted in the literature. It is our aim to show that $R$-matrix and monodromy matrix of the Hubbard…
We reconsider the basic properties of ray-transfer matrices for first-order optical systems from a geometrical viewpoint. In the paraxial regime of scalar wave optics, there is a wide family of beams for which the action of a ray-transfer…
While the Lorentz group serves as the basic language for Einstein's special theory of relativity, it is turning out to be the basic mathematical instrument in optical sciences, particularly in ray optics and polarization optics. The beam…
By expressing the time-independent Schrodinger equation in one dimension as a system of two first-order differential equations, the transfer matrix for a rectangular potential barrier is obtained making use of the matrix exponential. It is…
We present the geometry and symmetries of radiative transfer theory. Our geometrization exploits recent work in the literature that enables to obtain the Hamiltonian formulation of radiative transfer as the semiclassical limit of a phase…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
We develop a transfer matrix formalism for four-flux radiative transfer models, which is ideally suited for studying transport through multiple scattering layers. The model, derived for spherical particles within the diffusion…
We study the spectral properties of the transfer matrix for a gonihedric random surface model on a three-dimensional lattice. The transfer matrix is indexed by generalized loops in a natural fashion and is invariant under a group of motions…
Space-time modulation adds another powerful degree of freedom to the manipulation of classical wave systems. It opens the door for complex control of wave behavior beyond the reach of stationary systems, such as nonreciprocal wave transport…
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…
The transfer matrix method remains a simple yet powerful tool for modeling acoustic systems, particularly in a closed waveguide geometry. Here we present a generalisation of this method based on the theory of mode matching, that…
Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…
We give a pedagogical introduction to time-independent scattering theory in one dimension focusing on the basic properties and recent applications of transfer matrices. In particular, we begin surveying some basic notions of potential…
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional function space. We discuss its utility in…
The transfer-matrix method is a standard approach to wave propagation in stratified media. With the advent of cold-atom-based quantum and photonic technologies, several experiments and many proposals consider light propagation in…
We investigate the geometrical features of one-dimensional wave propagation, whose dynamics is described by the (2+1)-dimensional Lorentz group. We find many interesting geometrical ingredients such as spinorlike behavior of wave…