# Dynamical formulation of low-energy scattering in one dimension

@inproceedings{Loran2021DynamicalFO,
title={Dynamical formulation of low-energy scattering in one dimension},
year={2021}
}
• Published 11 February 2021
• Physics
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 leads to a dynamical formulation of stationary scattering. We explore the utility of this formulation in the study of the low-energy behavior of the scattering data. In particular, for the exponentially decaying potentials, we devise a simple iterative scheme for computing terms of arbitrary order…
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## References

SHOWING 1-10 OF 40 REFERENCES
A Dynamical Formulation of One-Dimensional Scattering Theory and Its Applications in Optics
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are
Transfermatrix in scattering theory: a survey of basic properties and recent developments
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
Solving scattering problems in the half-line using methods developed for scattering in the full line
Abstract We reduce the solution of the scattering problem defined on the half-line [ 0 , ∞ ) by a real or complex potential v ( x ) and a general homogeneous boundary condition at x = 0 to that of
Adiabatic series expansion and higher-order semiclassical approximations in scattering theory
The scattering properties of any complex scattering potential, , can be obtained from the dynamics of a particular non-unitary two-level quantum system . The application of the adiabatic
Low-energy behaviour of the scattering matrix for the Schrödinger equation on the line
For potentials whose first absolute moment exists the author proves continuity of the scattering matrix at zero energy. As a result he also obtains Levinson's theorem. He also studies the low-energy
Scattering theory for one-dimensional systems with ∝ dx V(x) = 0
• Mathematics
• 1987
Abstract Low-energy scattering for Schrodinger operators of the type H= −Δ + V in L2(R) with ∫Rdx V(x) = 0 is considered. The possibility of zero-energy eigenstates of H is taken into account
Delta-function potential with a complex coupling
We explore the Hamiltonian operator , where is the Dirac delta function and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a spectral singularity at . For Re(z) 0, H has
Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility
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
A Jost function description of zero-energy resonance and transparency effects in elastic collisions
• Physics
• 2013
Under certain circumstances, an elastic cross section at very low energies could differ by orders of magnitude above or below any reasonable estimate. The first case occurs near a zero-energy
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