Analogía magnetostática del estado de energía cero de Jackiw-Rebbi

Palabras clave: analogía, mecánica cuántica, modelo Jackiw-Rebbi, teoría magnetostática, transformación

Resumen

Se establece una analogía teórica entre la ecuación de Poisson y la ecuación de Dirac; específicamente, al estudiar el comportamiento del campo magnetostático, debido a la susceptibilidad en medios no homogéneos, no isotrópicos, unidimensionales, con alta permeabilidad magnética. Como resultado, se obtuvo una relación con el modelo de Jackiw-Rebbi para el estado de energía cero.

Biografía del autor/a

Robert Augusto Rubiano Giraldo, Universidade Federal de Campina Grande

Físico. Programa de Posgrado en Física, João Pessoa, Brasil.
Correo electrónico: robert.rubiano@academico.ufpb.br ORCID: https://orcid.org/0000-0003-3534-7832

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Biografía del autor/a

Robert Augusto Rubiano Giraldo, Universidade Federal de Campina Grande

Físico. Programa de Posgrado en Física, João Pessoa, Brasil.
Correo electrónico: robert.rubiano@academico.ufpb.br ORCID: https://orcid.org/0000-0003-3534-7832

Referencias bibliográficas

G. González, "Relation between Poisson and Schrödinger equations", American Journal of Physics, vol. 80, n.° 8, pp. 715-719, 2012. https://doi.org/10.1119/1.4722788

R. A. Rubiano, J. Tapia y H. González, "Dual solutions Schrödinger type for Poisson equation", Journal de Ciencia e Ingeniería, vol. 12, n.° 1, pp. 151-165, 2020. https://doi.org/10.46571/JCI.2020.1.14

V. Rokaj, F. Diakonos y G. Gabriel, "Comment on and erratum. Relation between Poisson and Schrödinger equations", American Journal of Physics, vol. 82, n.° 8, pp. 802-803, 2014. https://doi.org/10.1119/1.4884037

G. González, J. Méndez, R. Díaz y F. J. Gonzalez, "Electrostatic simulation of the Jackiw-Rebbi zero energy state", Revista Mexicana de Física E, vol. 65, n.° 1, pp. 30-33, 2019. https://doi.org/10.31349/RevMexFisE.65.30

M. A. Miri, M. Heinrich, R. El-Ganainy y D. N. Chris-todoulides, "Supersymmetric optical structures", Physical Review Letters, vol. 110, n.° 23, pp. 23-902, 2013. https://doi.org/10.1103/PhysRevLett.110.233902

M. Mohammad-Ali, H. Matthias, E. G. Ramy y C. Demetrios N., "Photonic simulation of topological excitations in metamaterials", Scientific Reports, vol. 4, n.° 3842, pp. 1-7, 2014. https://doi.org/10.1038/srep03842

L. Lamata, J. León y E. Solano, "dirac equation and quantum relativistic effects in a single trapped ion", Physical Review Letters, vol. 98, n.° 25, p. 253005, 2007. https://doi.org/10.1103/PhysRevLett.98.253005

S. Longhi, "Classical simulation of relativistic quantum mechanics in periodic optical structures", Applied Physics B, vol. 104, n.° 3, pp. 453-468, 2011. https://doi.org/10.1007/s00340-011-4628-7

P. A. M. Dirac, "The quantum theory of the electron", The Royal Society, vol. 117, n.° 778, pp. 610-624, 1928. https://doi.org/10.1098/rspa.1928.0023

K. Novoselov et al., "Two-dimensional gas of mass- less Dirac fermions in graphene", Nature, vol. 438, n.° 7065, pp. 197-200, 2005. https://doi.org/10.1038/nature04233

M. Hasan y C. Kane, "Colloquim: Topological insulators", Reviews of Modern Physics, vol. 438, n.° 7065, pp. 197-200, 2005.

X. Qi y S. Zhang, "Topological insulators and super- conductors", Reviews of Modern Physics, vol. 83, n.° 4, pp. 1057-1110, 2011. https://doi.org/10.1103/RevModPhys.83.1057

I. Aitchison y A. Hey, "In gauge theories in particle physics. A practical introduction", en Relativistic Quantum Mechanics. Nueva York, crc Press, 2012, pp. 63-83. https://doi.org/10.1201/b13717

P. A. M. Dirac, "A theory of electrons and protons", The Royal Society, vol. 126, n.° 801, pp. 360-365, 1930. https://doi.org/10.1098/rspa.1930.0013

C. D. Anderson, "The positive electron", Physical Re- view Journals Archive, vol. 43, n.° 1, pp. 491-494, 1933. https://doi.org/10.1103/PhysRev.43.491

R. P. Feynman, "The theory of positrons", Physical Re- view Journals Archive, vol. 76, n.° 1, pp. 749-759, 1949. https://doi.org/10.1103/PhysRev.76.749

N. Stander, N. Huard y D. Goldhaber, "Evidence for Klein tunneling in graphene", Physical Review Letters, vol. 102, n.° 026807, pp. 1-4, 2009. https://doi.org/10.1103/PhysRevLett.102.026807

M. Katsnelson, "Zitterbewgung chirality, and minimal conductivity in graphene", The European Physical Journal B, vol. 51, n.° 2, pp. 157-160, 2006. https://doi.org/10.1140/epjb/e2006-00203-1

R. Jackiw y C. Rebbi, "Solitons with fermion number 1/2", Physical Review D, vol. 13, n.° 12, pp. 3398-3409, 1976. https://doi.org/10.1103/PhysRevD.13.3398

R. Rajaraman y J. Bell, "On solitons with half integral charge", Physics Letters B, vol. 883, n.° 3213, pp. 256- 266, 1982.

F. Charmchi y S. Gousheh, "Massive Jackiw-Rebbi model", Nuclear Physics B, vol. 883, n.° 3213, pp. 151- 154, 1982. https://doi.org/10.1016/j.nuclphysb.2014.03.021

A. Amado y A. Mohammadi, "Coupled fermion-kink system in Jackiw-Rebbi", The European Physical Journal C, vol. 77, n.° 7, pp. 465-475, 2017. https://doi.org/10.1140/epjc/s10052-017-5044-x

D. Bazeia y A. Mohammadi, "Fermionic bound states in distinct kinklike", The European Physical Journal C, vol. 77, n.° 1434, pp. 203-211, 2017. https://doi.org/10.1140/epjc/s10052-017-4778-9

W. Su, J. Schrieffer y A. Heeger, "Soliton exitations in polyacetylene", Physical Review B, vol. 22, n.° 4, pp. 2099-2111, 1983. https://doi.org/10.1103/PhysRevB.22.2099

D. Mcmahon, Quantum mechanics demystified, New York: McGraw-Hill Education, 2013.

L. F. Charles, P. L. James y I. W. Michael, "Topologi- cally protected states in one-dimensional continuous systems and Dirac points", PNAS, vol. 111, n.° 24, pp. 8759-8763, 2014. https://doi.org/10.1073/pnas.1407391111

K. Alexei, "Periodic table for topological insulators and superconductors", AIP Conference Proceedings, vol. 1134, n.° 1, pp. 22-30, 2009.

A. Altland y M. R. Zirnbauer, "Nonstandard sym- metry classes in mesoscopic normal-superconduc- ting hybrid structures", Phys. Rev. B, vol. 55, n.° 2, pp. 1142-1161, 1997. https://doi.org/10.1103/PhysRevB.55.1142

F. Charmchi y S. Gousheh, "Massive Jackiw-Rebbi model", Nuclear Physics B, vol. 883, n.° 3213, pp. 256- 266, 2014. https://doi.org/10.1016/j.nuclphysb.2014.03.021

M. Sadiku, Elementos de Electromagnetismo, 3.a ed. México: Oxford University Press, 2003.

I. Irodov, Basic laws of electromagnetism. Nueva Delhi: CBS Publishers & Distributiors, 1994.

J. Griffiths, Introduction to electrodynamics, 4.a ed. Nueva York: Cambridge University Press, 2017. https://doi.org/10.1017/9781108333511

A. Lenard, "Exact statistical mechanics of a one-dimensional system with Coulomb forces", Journal of Mathematical Physics, vol. 2, n.° 5, pp. 682-693, 1961. https://doi.org/10.1063/1.1703757

C. Heck, Magnetic Materials and their Applications. Londres: Butterworth-Heinemann, 1974. https://doi.org/10.1016/B978-0-408-70399-4.50015-6

E. Snelling, Soft ferrites. Properties and applications. Londres: Ilifee, 1969.

Cómo citar
Rubiano Giraldo, R. A. (2021). Analogía magnetostática del estado de energía cero de Jackiw-Rebbi. Revista Facultad De Ciencias Básicas, 17(1), 47–56. https://doi.org/10.18359/rfcb.4992
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2021-11-19
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