Transforming kinks into compactons in the \(O(3)\)-sigma model. (English) Zbl 1448.81426
Summary: In this work, we investigate the solutions of vortices in the \(O(3)\)-sigma model with the gauge field governed by the Chern-Simons term and subject to a hyperbolic self-dual potential. We show that this model admits both topological and nontopological soliton solutions. Employing numerical analysis, we realize that the topological solutions of the model can be transformed into compacton-like solutions. On the other hand, after modifying the model by the introduction of a dielectric constant, an exciting feature appears; namely, the nontopological solutions can be transformed into kink-like solutions through the numerical variation of the dielectric constant. Furthermore, we discuss the degeneracy for the topological solitons in a given sector. Finally, we present the numerical solutions of the first model.
MSC:
| 81T10 | Model quantum field theories |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 35Q40 | PDEs in connection with quantum mechanics |
| 35C08 | Soliton solutions |
References:
| [1] | Belavin, A. A.; Polyakov, A. M., JETP Lett., 22, 245 (1975) |
| [2] | Ghosh, P. K.; Ghosh, S. K., Phys. Lett. B, 366, 199 (1996) |
| [3] | Cunha, M. S.; Landim, R. R.; Almeida, C. A.S., Phys. Rev. D, 74, Article 067701 pp. (2006) |
| [4] | Samoilenka, A.; Shnir, Y., Phys. Rev. D, 95, Article 045002 pp. (2017) |
| [5] | Lee, C.; Lee, K.; Min, H., Phys. Lett. B, 252, 79 (1990) |
| [6] | Wilczek, F., Phys. Rev. Lett., 49, 957 (1982) |
| [7] | Laughlin, R. B., Phys. Rev. Lett., 50, 1395 (1983) |
| [8] | Cavalcante, F. S.A.; Cunha, M. S.; Almeida, C. A.S., Phys. Lett. B, 475, 315 (2000) · Zbl 1049.81552 |
| [9] | Horvathya, P.; Zhang, P., Phys. Rep., 481, 83 (2009) |
| [10] | Haldane, F. D.M., Phys. Rev. Lett., 67, 937 (1991) · Zbl 0990.81534 |
| [11] | Zhang, S. C., Internat. J. Modern Phys. B, 06, 803 (1992) |
| [12] | Casana, R.; Dias, M. L.; da Hora, E., Phys. Lett. B, 768, 254 (2017) · Zbl 1370.70052 |
| [13] | Leblond, H., J. Phys. A, 31, 5129 (1998) · Zbl 0953.78006 |
| [14] | Christodoulides, D. N.; Joseph, R. I., Opt. Lett., 13, 794 (1988) |
| [15] | Eisenberg, H. S.; Silberberg, Y.; Morandotti, R.; Boyd, A. R.; Aitchinson, J. S., Phys. Rev. Lett., 81, 3383 (1998) |
| [16] | Morandotti, R.; Eisenberg, H. S.; Silberberg, Y.; Sorel, M.; Aitchison, J. S., Phys. Rev. Lett., 86, 3296 (2000) |
| [17] | Fleischer, J. W.; Segev, M.; Efremidis, N. K.; Christodoulides, D. N., Lett. Nat., 422, 147 (2003) |
| [18] | Leese, R. A., Nuclear Phys. B, 366, 283 (1991) |
| [19] | Lee, K., Phys. Rev. D, 49, 4265 (1994) |
| [20] | Casana, R.; Lazar, G.; Sourrouille, L., Adv. High Energy Phys., 2018, Article 4281939 pp. (2018) · Zbl 1404.81167 |
| [21] | Bazeia, D.; Lima, E. E.M.; Losano, L., Eur. Phys. J. C, 76, 418 (2016) |
| [22] | Bazeia, D.; Vassilevich, D. V., Phys. Rev. D, 91, Article 047701 pp. (2015) |
| [23] | Rosenau, P.; Hyman, J. M., Phys. Rev. Lett., 70, 564 (1993) · Zbl 0952.35502 |
| [24] | Nielsen, H.; Olesen, P., Nuclear Phys. B, 61, 1064 (1973) |
| [25] | Jubert, P.-O.; Allenspach, R.; Bischof, A., Phys. Rev. B, 69, 220410(R) (2004) |
| [26] | Romming, N.; Hanneken, C.; Menzel, M.; Bickel, J. E.; Wolter, B.; von Bergmann, K.; Wiesendanger, R., Science, 341, 636 (2013) |
| [27] | Veras, D. F.S.; Cruz, W. T.; Maluf, R. V.; Almeida, C. A.S., Phys. Lett. B, 754, 201 (2017) |
| [28] | Cavalcante, F. S.A.; Ribeiro Filho, J.; Nogueira Filho, R.; Almeida, C. A.S.; Freire, V. N., Phys. Rev. B, 55, 1326 (1997) |
| [29] | de Souza Dutra, A.; Almeida, C. A.S., Phys. Lett. A, 275, 25 (2000) · Zbl 1115.81396 |
| [30] | Bastard, G., Les ed. Phys., 66, 707 (1988) |
| [31] | Bazeia, D.; Belendryasova, E.; Gani, V. A., Eur. Phys. J. C, 78, 1-14 (2018) |
| [32] | Bazeia, D.; Gomes, A. R.; Nobrega, K. Z.; Simas, F. C., Internat. J. Modern Phys. A, 34, Article 1950200 pp. (2019) |
| [33] | Ruffini, R.; Wheeler, J. A., Phys. Today, 24, 30 (1971) |
| [34] | Bizon, P., Acta Phys. Polon. B, 25, 877 (1994) · Zbl 0966.83526 |
| [35] | Bogomol’nyi, E. B., Yad. Fiz., 24, 861-870 (1976) |
| [36] | Atmaja, N. A.; Ramadhan, H. S., Phys. Rev. D, 90, Article 105009 pp. (2014) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
