# Dynamical formulation of low-energy scattering in one dimension

@inproceedings{Loran2021DynamicalFO, title={Dynamical formulation of low-energy scattering in one dimension}, author={Farhang Loran and Ali Mostafazadeh}, year={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 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…

## 3 Citations

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## References

SHOWING 1-10 OF 40 REFERENCES

A Dynamical Formulation of One-Dimensional Scattering Theory and Its Applications in Optics

- Physics, Mathematics
- 2014

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

- 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…

Solving scattering problems in the half-line using methods developed for scattering in the full line

- Physics, Mathematics
- 2019

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

- Physics, Mathematics
- 2014

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

- Mathematics
- 1988

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

- Mathematics, Physics
- 2006

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

- 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…

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…