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…
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References
SHOWING 1-10 OF 57 REFERENCES
A Dynamical Formulation of One-Dimensional Scattering Theory and Its Applications in Optics
- Mathematics
- 2014
Transfer matrices as nonunitary S matrices, multimode unidirectional invisibility, and perturbative inverse scattering
- Mathematics, Physics
- 2014
We show that in one dimension the transfer matrix M of any scattering potential v coincides with the S-matrix of an associated time-dependent non-Hermitian 2 x 2 matrix Hamiltonian H(\tau). If v is…
Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility
- Physics, Mathematics
- 2014
The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the $S$-matrix of a two-level time-dependent non-Hermitian Hamiltonian H(t). We show that…
Perturbative Unidirectional Invisibility
- Physics
- 2015
We outline a general perturbative method of evaluating scattering features of finite-range complex potentials and use it to examine complex perturbations of a rectangular barrier potential. In…
Quantum scattering in two dimensions
- Physics
- 1986
A self‐contained discussion of nonrelativistic quantum mechanical potential scattering in two dimensions is presented. The discussion includes, among other topics, partial wave decomposition in…
Active Invisibility Cloaks in One Dimension
- Mathematics
- 2015
We outline a general method of constructing finite-range cloaking potentials which render a given finite-range real or complex potential $v(x)$ unidirectionally reflectionless or invisible at a…
Renormalized contact potential in two dimensions
- Physics
- 1998
We obtain for the attractive Dirac δ-function potential in two-dimensional quantum mechanics a renormalized formulation that avoids reference to a cutoff and running coupling constant. Dimensional…
Unidirectionally invisible potentials as local building blocks of all scattering potentials
- Mathematics
- 2014
We give a complete solution of the problem of constructing a scattering potential $v(x)$ that possesses scattering properties of one's choice at an arbitrary prescribed wave number. Our solution…