Resonant transmission in one-dimensional quantum mechanics with two independent point interactions: Full parameter analysis

@article{Konno2017ResonantTI,
  title={Resonant transmission in one-dimensional quantum mechanics with two independent point interactions: Full parameter analysis},
  author={Kohkichi Konno and Tomoaki Nagasawa and Rohta Takahashi},
  journal={Annals of Physics},
  year={2017},
  volume={385},
  pages={729-743}
}
Abstract We discuss the scattering of a quantum particle by two independent successive point interactions in one dimension. The parameter space for two point interactions is given by U ( 2 ) × U ( 2 ) , which is described by eight real parameters. We perform an analysis of perfect resonant transmission on the whole parameter space. By investigating the effects of the two point interactions on the scattering matrix of plane wave, we find the condition under which perfect resonant transmission… 
View PDF on arXiv
4 Citations
Methods Citations
1

Figures from this paper

4 Citations

Citation Type

Citation Type

Quantum reflection and transmission in ring systems with double Y-junctions: occurrence of perfect reflection
We consider the scattering problems of a quantum particle in a system with a single Y-junction and in ring systems with double Y-junctions. We provide new formalism for such quantum mechanical…
Origin of resonant tunneling through single-point barriers
  • A. Zolotaryuk
  • Physics, Mathematics
    Physica E: Low-dimensional Systems and Nanostructures
  • 2018
Abstract The physical interpretation of the appearance of resonant transmission through single-point barriers is discussed on the basis of a double-layer heterostructure in the squeezing limit as…
A phenomenon of splitting resonant-tunneling one-point interactions
The so-called $\delta'$-interaction as a particular example in Kurasov's distribution theory developed on the space of discontinuous (at the point of singularity) test functions, is identified with…
Point Interactions With Bias Potentials
We develop an approach on how to define single-point interactions under the application of external fields. The essential feature relies on an asymptotic method based on the one-point approximation…

References

SHOWING 1-10 OF 53 REFERENCES
Effects of Two Successive Parity-Invariant Point Interactions on One-Dimensional Quantum Transmission: Resonance Conditions for the Parameter Space
We consider the scattering of a quantum particle by two independent, successive parity-invariant point interactions in one dimension. The parameter space for the two point interactions is given by…
Resonant Transmission in One-Dimensional Quantum Systems with Two Parity-Invariant Point Interactions
We discuss one-dimensional quantum systems with two parity-invariant point interactions within the framework of quantum mechanics. By investigating the conditions under which resonant transmission…
Double General Point Interactions: Symmetry and Tunneling Times
We consider the one dimensional problem of a non-relativistic quantum particle scattering off a double barrier built from two generalized point interactions (each one characterized as a member of the…
Fermion-Boson Duality of One-Dimensional Quantum Particles with Generalized Contact Interactions
For a system of spinless one-dimensional fermions, the nonvanishing short-range limit of a two-body interaction is shown to induce the wave-function discontinuity. We prove the equivalence of this…
Scattering properties of point dipole interactions
The scattering properties of a three-parameter family of point dipole-like interactions constructed from a sequence of barrier-well rectangles are studied in the zero-range limit. Besides the real…
Green functions for generalized point interactions in one dimension: A scattering approach
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, require some sort of regularization…
Supersymmetry in quantum mechanics with point interactions
We investigate supersymmetry in one-dimensional quantum mechanics with point interactions. We clarify a class of point interactions compatible with supersymmetry and present N=2 supersymmetric models…
Symmetry, Duality, and Anholonomy of Point Interactions in One Dimension
Abstract We analyze the spectral structure of a one-dimensional quantum mechanical system with point interaction, which is known to be parametrized by the group U(2). Based on the classification of…
Non-Abelian Monopole in the Parameter Space of Point-like Interactions
We study non-Abelian geometric phase in $\mathscr{N} = 2$ supersymmetric quantum mechanics for a free particle on a circle with two point-like interactions at antipodal points. We show that…
INTRINSIC RESONANT TUNNELING PROPERTIES OF THE ONE-DIMENSIONAL SCHRÖDINGER OPERATOR WITH A DELTA DERIVATIVE POTENTIAL
Restricting ourselves to a simple rectangular approximation but using properly a two-scale regularization procedure, additional resonant tunneling properties of the one-dimensional Schrodinger…
...
1
2
3
4
5
...