P L Christiansen et al 2003 J. Phys. A: Math. Gen. 36 7589 doi:10.1088/0305-4470/36/27/311
On the existence of resonances in the transmission probability for interactions arising from derivatives of Dirac's delta function
P L Christiansen1, H C Arnbak1, A V Zolotaryuk1,2, V N Ermakov1,2 and Y B Gaididei1,2
Show affiliationsThe scattering properties of regularizing finite-range potentials constructed in the form of squeezed rectangles, which approximate the first and second derivatives of the Dirac delta function δ(x), are studied in the zero-range limit. Particularly, for a countable set of interaction strength values, a non-zero transmission through the point potential δ'(x), defined as the weak limit (in the standard sense of distributions) of a special dipole-like sequence of rectangles, is shown to exist when the rectangles are squeezed to zero width. A tripole sequence of rectangles, which gives in the weak limit the distribution δ''(x), is demonstrated to exhibit the total transmission for a countable sequence of the rectangle's width that tends to zero. However, this tripole sequence does not admit a well-defined point interaction in the zero-range limit, making sense only for a finite range of the regularizing rectangular-like potentials.
- PACS
- MSC
-
81Uxx Scattering theory (See also 34A55, 34L25, 34L40, 35P25, 47A40)
- Subjects
- Dates
-
Issue 27 (11 July 2003)
Received 3 March 2003, in final form 23 May 2003
Published 25 June 2003
-
On the existence of resonances in the transmission probability for interactions arising from derivatives of Dirac's delta function
P L Christiansen et al 2003 J. Phys. A: Math. Gen. 36 7589
-
Supersymmetry and geometric motion
L J Boya et al 1993 J. Phys. A: Math. Gen. 26 5825
-
Spin-fluctuation theory of quasi-two-dimensional itinerant-electron ferromagnets
Yoshinori Takahashi 1997 J. Phys.: Condens. Matter 9 10359
-
A tribute to Yuri Klimontovich
Radu Balescu et al 2005 J. Phys.: Conf. Ser. 11
-
On the strength of the carbon nanotube-based space elevator cable: from nanomechanics to megamechanics
Nicola M Pugno 2006 J. Phys.: Condens. Matter 18 S1971
-
Nanocomposite electrode materials for high energy density rechargeable lithium batteries
S J Kim et al 2007 Phys. Scr. 2007 57
-
Local Hanle-effect studies of spin drift and diffusion in n:GaAs epilayers and spin-transport devices
M Furis et al 2007 New J. Phys. 9 347
-
Stability and analysis of configuration-tunable bi-directional MWNT bearings
A Subramanian et al 2009 Nanotechnology 20 495704
-
A large-area nanoscale gold hemisphere pattern as a nanoelectrode array
Huaqing Li and Nianqiang Wu 2008 Nanotechnology 19 275301
-
Population inversion of nuclear states by a Penning trap mass spectrometer
K. Blaum et al 2004 Europhys. Lett. 67 586
Users also read
What's this?Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Spectral problems in open quantum chaos
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories
super-Yang–Mills*