PL EN


Preferences help
enabled [disable] Abstract
Number of results
2017 | 132 | 4 | 1351-1357
Article title

Weakly Bound States in Heterogeneous Waveguides: A Calculation to Fourth Order

Authors
Content
Title variants
Languages of publication
EN
Abstracts
EN
We have extended a previous calculation of the energy of a weakly heterogeneous waveguide to fourth order in the density perturbation, deriving its general expression. For particular configurations where the second and third orders both vanish, we discover that the fourth order contribution lowers in general the energy of the state, below the threshold of the continuum. In these cases the waveguide possesses a localized state. We have applied our general formula to a solvable model with vanishing second and third orders reproducing the exact expression for the fourth order.
Publisher

Year
Volume
132
Issue
4
Pages
1351-1357
Physical description
Dates
published
2017-10
received
2017-01-23
(unknown)
2017-09-25
Contributors
author
  • Facultad de Ciencias, CUICBAS, Universidad de Colima, Bernal Díaz del Castillo 340, Colima, Colima, Mexico
References
  • [1] P. Exner, P. Seba, J. Math. Phys. 30, 2574 (1989), doi: 10.1063/1.528538
  • [2] J. Goldstone, R.L. Jaffe, Phys. Rev. B 45, 14100 (1992), doi: 10.1103/PhysRevB.45.14100
  • [3] R.L. Schult, D.G. Ravenhall, H.W. Wyld, Phys. Rev. B 39, 5476 (1989), doi: 10.1103/PhysRevB.39.5476
  • [4] S. Qu, M.R. Geller, Phys. Rev. B 70, 085414 (2004), doi: 10.1103/PhysRevB.70.085414
  • [5] F. Ursell, Proc. Camb. Philos. Soc. 47, 348 (1951), doi: 10.1017/S0305004100026700
  • [6] F. Ursell, Proc. R. Soc. Lond. A 214, 79 (1952), doi: 10.1098/rspa.1952.0152
  • [7] W. Bulla, F. Gesztesy, W. Renger, B. Simon, Proc. Am. Math. Soc. 125, 1487 (1997), doi: 10.1090/S0002-9939-97-03726-X
  • [8] P. Exner, S.A. Vugalter, Lett. Math. Phys. 39, 59 (1997), doi: 10.1023/A:100737321
  • [9] P. Amore, F.M. Fernández, C.P. Hofmann, Europ. Phys. J. B 89, 163 (2016), doi: 10.1140/epjb/e2016-70197-0
  • [10] G. Gat, B. Rosenstein, Phys. Rev. Lett. 70, 5 (1993), doi: 10.1103/PhysRevLett.70.5
  • [11] P. Amore, J.P. Boyd, F.M. Fernández, M. Jacobo, P. Zhevandrov, The Anziam Journal 1, 15 (2017), doi: 10.1017/S1446181117000293
  • [12] Y. Avishai, D. Bessis, B.G. Giraud, G. Mantica, Phys. Rev. B 44, 233101 (1991), doi: 10.1103/PhysRevB.44.8028
  • [13] P. Amore, J. Math. Phys. 51, 052105 (2010), doi: 10.1063/1.3364792
  • [14] P. Amore, arXiv: 1601.02470 (2016) http://arXiv.org/abs/1601.02470
  • [15] P. Amore, F.M. Fernández, Ann. Phys. 378, 253 (2017), doi: 10.1016/j.aop.2017.01.022
  • [16] Till Tantau, The TikZ and PGF Packages, Manual for version 3.0.0 http://sourceforge.net/projects/pgf/
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv132n4p25kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.