# Transfer matrix formulation of scattering theory in two and three dimensions

@article{Loran2016TransferMF, title={Transfer matrix formulation of scattering theory in two and three dimensions}, author={Farhang Loran and Ali Mostafazadeh}, journal={Physical Review A}, year={2016}, volume={93}, pages={042707} }

In one dimension one can dissect a scattering potential $ v(x) $ into pieces $ v_i(x) $ and use the notion of the transfer matrix to determine the scattering content of $ v(x) $ from that of $ v_i(x) $. This observation has numerous practical applications in different areas of physics. The problem of finding an analogous procedure in dimensions larger than one has been an important open problem for decades. We give a complete solution for this problem and discuss some of its applications. In…

## 22 Citations

Fundamental transfer matrix and dynamical formulation of stationary scattering in two and three dimensions

- PhysicsPhysical Review A
- 2021

We offer a consistent dynamical formulation of stationary scattering in two and three dimensions that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear…

Transfermatrix in scattering theory: a survey of basic properties and recent developments

- Physics, MathematicsTURKISH JOURNAL OF PHYSICS
- 2020

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…

Transfer-matrix formulation of the scattering of electromagnetic waves and broadband invisibility in three dimensions

- Physics
- 2019

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…

Exactness of the Born approximation and broadband unidirectional invisibility in two dimensions

- Physics, Mathematics
- 2019

Achieving exact unidirectional invisibility in a finite frequency band has been an outstanding problem for many years. We offer a simple solution to this problem in two dimensions that is based on…

Exact solution of the two-dimensional scattering problem for a class of δ-function potentials supported on subsets of a line

- Physics, MathematicsJournal of Physics A: Mathematical and Theoretical
- 2018

We use the transfer matrix formulation of scattering theory in two-dimensions to treat the scattering problem for a potential of the form $v(x,y)=\zeta\,\delta(ax+by)g(bx-ay)$ where $\zeta,a$, and…

Scattering Theory and PT-Symmetry

- 2018

We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their P-, T -, and PT -symmetries. In particular, we…

Dynamical formulation of low-energy scattering in one dimension

- Physics
- 2021

The transfer matrix M of a short-range potential may be expressed in terms of the timeevolution operator for an effective two-level quantum system with a time-dependent nonHermitian Hamiltonian. This…

Nonlinear scattering and its transfer matrix formulation in one dimension

- Physics, MathematicsThe European Physical Journal Plus
- 2019

Abstract.We present a systematic formulation of the scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition…

Geometric scattering of a scalar particle moving on a curved surface in the presence of point defects

- Physics, MathematicsAnnals of Physics
- 2019

A nonrelativistic scalar particle that is constrained to move on an asymptotically flat curved surface undergoes a geometric scattering that is sensitive to the mean and Gaussian curvatures of the…

Scattering by a collection of δ-function point and parallel line defects in two dimensions

- Physics, MathematicsAnnals of Physics
- 2021

Interaction of waves with point and line defects are usually described by δ-function potentials supported on points or lines. In two dimensions, the scattering problem for a finite collection of…

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