Potentials with identical scattering properties below a critical energy

Loran, Farhang; Mostafazadeh, Alí

doi:10.1063/1.5054759

Cited by 5 publications

(11 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result has found interesting applications in addressing a number of basic problems of scattering theory [61][62][63][64][65][66][67][68][69].…”

Section: Potential Scattering and Its Dynamical Formulationmentioning

confidence: 90%

Transmission of low-energy scalar waves through a traversable wormhole

2020

Self Cite

View full text Add to dashboard Cite

We study the scattering of low-energy massless and massive minimally coupled scalar fields by an asymptotically flat traversable wormhole. We provide a comprehensive treatment of this problem offering analytic expressions for the transmission and reflection amplitudes of the corresponding effective potential and the absorption cross section of the wormhole. Our results, which are based on a recently developed dynamical formulation of time-independent scattering theory, apply to a large class of wormhole spacetimes including a wormhole with a sharp transition, the Ellis wormhole, and a family of its generalizations.

show abstract

“…This result has found interesting applications in addressing a number of basic problems of scattering theory [61][62][63][64][65][66][67][68][69].…”

Section: Potential Scattering and Its Dynamical Formulationmentioning

confidence: 90%

Transmission of low-energy scalar waves through a traversable wormhole

2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…In particular, we can express it as the time-ordered exponential of a pseudo-normal Hamiltonian operator and use it to address a number of previously unsolved basic problems of scattering theory. Among these are a singularity-free treatment of the single-and multi-delta-function potentials in two and three dimensions [123,134], the discovery of a new class of exactly-solvable scattering potentials with potential applications in laser optics and quantum computation [135], the first theoretical realization of exact omnidirectional [136] and unidirectional invisibility [137] in a finite spectral band [k − , k + ], the characterization of scattering potential with identical scattering properties below a prescribed wavenumber [138], the introduction of the quasiexactly solvable scattering potentials, and the discovery of the scattering potentials for which the first Born approximation is exact [137].…”

Section: Discussionmentioning

confidence: 99%

“…If we plug (144) and (145) in (138) and demand that the resulting equation holds independently of the choice of ψ(x), we obtain a linear system of four algebraic equations for the entries of the matrix Hamiltonian H(x). Solving this system, we find [111]…”

Section: Potential Scattering As a Dynamical Phenomenonmentioning

confidence: 99%

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

Mostafazadeh¹

2020

Turk J Phys

Self Cite

View full text Add to dashboard Cite

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 scattering such as transfer matrix and its analyticity, multi-delta-function and locally periodic potentials, Jost solutions, spectral singularities and their time-reversal, and unidirectional reflectionlessness and invisibility. We then offer a simple derivation of the Lippmann-Schwinger equation and Born series, and discuss the Born approximation. Next, we outline a recently developed dynamical formulation of timeindependent scattering theory in one dimension. This formulation relates the transfer matrix and therefore the solution of the scattering problem for a given potential to the solution of the time-dependent Schrödinger equation for an effective non-unitary two-level quantum system. We provide a self-contained treatment of this formulation and some of its most important applications. Specifically, we use it to devise a powerful alternative to the Born series and Born approximation, derive dynamical equations for the reflection and transmission amplitudes, discuss their application in constructing exact tunable unidirectionally invisible potentials, and use them to provide an exact solution for single-mode inverse scattering problems. The latter, which has important applications in designing optical devices with a variety of functionalities, amounts to providing an explicit construction for a finite-range complex potential whose reflection and transmission amplitudes take arbitrary prescribed values at any given wavenumber.

show abstract

“…We also recall that T l/r ± belong to the function space F 4 k , and the EM transfer matrix M is a linear operator acting in this space. In view of (63) and (64), the invisibility condition,…”

Section: Perfect Broadband Invisibilitymentioning

confidence: 99%

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

Loran¹,

Mostafazadeh²

2020

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

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 M that does not involve slicing of the scattering medium or discretization of some of the position-or momentum-space variables. This is a linear operator that we can express as a 4 × 4 matrix with operator entries and identify with the S-matrix of an effective nonunitary quantum system. We use this observation to establish the composition property of M, obtain an exact solution of the scattering problem for a non-magnetic point scatterer that avoids the divergences of the Green's function approaches, and prove a general invisibility theorem. The latter allows for an explicit characterization of a class of isotropic media M displaying perfect broadband invisibility for electromagnetic waves of arbitrary polarization provided that their wavenumber k does not exceed a preassigned critical value α, i.e., M behaves exactly like vacuum for k ≤ α. Generalizing this phenomenon, we introduce and study α-equivalent media that, by definition, have identical scattering features for

show abstract

Potentials with identical scattering properties below a critical energy

Cited by 5 publications

References 26 publications

Transmission of low-energy scalar waves through a traversable wormhole

Transmission of low-energy scalar waves through a traversable wormhole

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

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

Contact Info

Product

Resources

About