Alí Mostafazadeh
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View article: Low-frequency scattering of TE and TM waves by an inhomogeneous medium with planar symmetry
Low-frequency scattering of TE and TM waves by an inhomogeneous medium with planar symmetry Open
Stationary scattering of TE and TM waves propagating in an isotropic medium with planar symmetry is described by Bergmann’s equation in one dimension. This is a generalization of Helmholtz equation which allows for developing transfer matr…
View article: Pseudo-Hermiticity, Anti-Pseudo-Hermiticity, and Generalized Parity-Time-Reversal Symmetry at Exceptional Points
Pseudo-Hermiticity, Anti-Pseudo-Hermiticity, and Generalized Parity-Time-Reversal Symmetry at Exceptional Points Open
For a diagonalizable linear operator $H:\mathscr{H}\to\mathscr{H}$ acting in a separable Hilbert space $\mathscr{H}$, i.e., an operator with a purely point spectrum, eigenvalues with finite algebraic multiplicities, and a set of eigenvecto…
View article: Scattering of Transverse Electric and Transverse Magnetic Waves and Quantum Dynamics Generated by non-Hermitian Hamiltonians
Scattering of Transverse Electric and Transverse Magnetic Waves and Quantum Dynamics Generated by non-Hermitian Hamiltonians Open
The study of the scattering of electromagnetic waves by a linear isotropic medium with planar symmetry can be reduced to that of their transverse electric (TE) and transverse magnetic (TM) modes. For situations where the medium consists of…
View article: Dynamical formulation of low-frequency scattering in two and three dimensions
Dynamical formulation of low-frequency scattering in two and three dimensions Open
The transfer matrix of scattering theory in one dimension can be expressed in terms of the time-evolution operator for an effective non-unitary quantum system. In particular, it admits a Dyson series expansion which turns out to facilitate…
View article: Scattering of TE and TM waves and quantum dynamics generated by non-Hermitian Hamiltonians
Scattering of TE and TM waves and quantum dynamics generated by non-Hermitian Hamiltonians Open
The study of the scattering of electromagnetic waves by a linear isotropic medium with planar symmetry can be reduced to that of their TE and TM modes. For situations where the medium consists of parallel homogeneous slabs, one may use the…
View article: Can Nth order Born approximation be exact?
Can Nth order Born approximation be exact? Open
For the scattering of scalar waves in two and three dimensions and electromagnetic waves in three dimensions, we identify a condition on the scattering interaction under which the N th order Born approximation gives the exact solution of t…
View article: Consistent Treatment of Quantum Systems with a Time-Dependent Hilbert Space
Consistent Treatment of Quantum Systems with a Time-Dependent Hilbert Space Open
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-indepe…
View article: Consistent Treatment of Quantum Systems with a Time-Dependent Hilbert Space
Consistent Treatment of Quantum Systems with a Time-Dependent Hilbert Space Open
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-indepe…
View article: Exactness of the First Born Approximation in Electromagnetic Scattering
Exactness of the First Born Approximation in Electromagnetic Scattering Open
For the scattering of plane electromagnetic waves by a general possibly anisotropic stationary linear medium in three dimensions, we give a condition on the permittivity and permeability tensors of the medium under which the first Born app…
View article: Introducing a general method for solving electromagnetic radiation problem in an arbitrary linear medium
Introducing a general method for solving electromagnetic radiation problem in an arbitrary linear medium Open
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…
View article: Broadband directional invisibility
Broadband directional invisibility Open
The discovery of unidirectional invisibility and its broadband realization in optical media satisfying spatial Kramers-Kronig relations are important landmarks of non-Hermitian photonics. We offer a precise characterization of a higher-dim…
View article: Exactness of the first Born approximation in electromagnetic scattering
Exactness of the first Born approximation in electromagnetic scattering Open
For the scattering of plane electromagnetic waves by a general possibly anisotropic stationary linear medium in three dimensions, we give a condition on the permittivity and permeability tensors of the medium under which the first Born app…
View article: Fundamental transfer matrix for electromagnetic waves, scattering by a planar collection of point scatterers, and anti-PT-symmetry
Fundamental transfer matrix for electromagnetic waves, scattering by a planar collection of point scatterers, and anti-PT-symmetry Open
We develop a fundamental transfer-matrix formulation of the scattering of electromagnetic (EM) waves that incorporates the contribution of the evanescent waves and applies to general stationary linear media which need not be isotropic, hom…
View article: Existence of the transfer matrix for a class of nonlocal potentials in two dimensions
Existence of the transfer matrix for a class of nonlocal potentials in two dimensions Open
Evanescent waves are waves that decay or grow exponentially in regions of the space void of interaction. In potential scattering defined by the Schrödinger equation, $(-\nabla^2+v)ψ=k^2ψ$ for a local potential $v$, they arise in dimensions…
View article: Singularity-free treatment of delta-function point scatterers in two dimensions and its conceptual implications
Singularity-free treatment of delta-function point scatterers in two dimensions and its conceptual implications Open
In two dimensions, the standard treatment of the scattering problem for a delta-function potential, , leads to a logarithmic singularity which is subsequently removed by a renormalization of the coupling constant . Recentl…
View article: Transfer matrix formulation of stationary scattering in 2D and 3D: A concise review of recent developments
Transfer matrix formulation of stationary scattering in 2D and 3D: A concise review of recent developments Open
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 …
View article: Comment on "Scattering of light by a parity-time-symmetric dipole beyond the first Born approximation"
Comment on "Scattering of light by a parity-time-symmetric dipole beyond the first Born approximation" Open
In [J. A. Rebouças and P. A. Brandão, Phys. Rev. A 104, 063514 (2021)] the authors compute the scattering amplitude for a $\mathcal{P}\mathcal{T}$-symmetric double-delta-function potential in three dimensions by invoking the far-zone appro…
View article: Propagating-wave approximation in two-dimensional potential scattering
Propagating-wave approximation in two-dimensional potential scattering Open
We introduce a nonperturbative approximation scheme for performing scattering calculations in two dimensions that involves neglecting the contribution of the evanescent waves to the scattering amplitude. This corresponds to replacing the i…
View article: Exceptional points and pseudo-Hermiticity in real potential scattering
Exceptional points and pseudo-Hermiticity in real potential scattering Open
We employ a recently-developed transfer-matrix formulation of scattering theory in two dimensions to study a class of scattering setups modeled by real potentials. The transfer matrix for these potentials is related to the time-evolution o…
View article: Transfer matrix formulation of stationary scattering in 2D and 3D: A concise review of recent developments
Transfer matrix formulation of stationary scattering in 2D and 3D: A concise review of recent developments Open
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 …
View article: Report on scipost_202109_00035v2
Report on scipost_202109_00035v2 Open
We employ a recently-developed transfer-matrix formulation of scattering theory in two dimensions to study a class of scattering setups modeled by real potentials.The transfer matrix for these potentials is related to the time-evolution op…
View article: Report on scipost_202109_00035v1
Report on scipost_202109_00035v1 Open
We employ a recently-developed transfer-matrix formulation of scattering theory in two dimensions to study a class of scattering setups modeled by real potentials.The transfer matrix for these potentials is related to the time-evolution op…
View article: Report on scipost_202109_00035v1
Report on scipost_202109_00035v1 Open
We employ a recently-developed transfer-matrix formulation of scattering theory in two dimensions to study a class of scattering setups modeled by real potentials.The transfer matrix for these potentials is related to the time-evolution op…
View article: Scattering by a collection of $\delta$-function point and parallel line defects in two dimensions
Scattering by a collection of $\delta$-function point and parallel line defects in two dimensions Open
Interaction of waves with point and line defects are usually described by $\delta$-function potentials supported on points or lines. In two dimensions, the scattering problem for a finite collection of point defects or parallel line defect…
View article: Fundamental transfer matrix and dynamical formulation of stationary scattering in two and three dimensions
Fundamental transfer matrix and dynamical formulation of stationary scattering in two and three dimensions Open
We offer a consistent dynamical formulation of stationary scattering in two and three dimensions (2D and 3D) that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear operator acting in an infinit…
View article: Dynamical formulation of low-energy scattering in one dimension
Dynamical formulation of low-energy scattering in one dimension Open
The transfer matrix M of a short-range potential may be expressed in terms of the time-evolution operator for an effective two-level quantum system with a time-dependent non-Hermitian Hamiltonian. This leads to a dynamical formulation of s…