Software para la simulación del estado fundamental (ground state) de solitones de ondas de materia
DOI:
https://doi.org/10.30973/progmat/2013.5.2/10Keywords:
solitary waves, soliton, ground stateAbstract
This paper reports the results of systematic studies of matter-wave solitons in two dimensions, and it is shown that both the calculation and the stability of a solitary wave can be obtained. This research was done by optimizing the Accelerated imaginary time evolution method (AITEM) originally implemented by physicists Yang and Lakoba using Matlab. In this research, AITEM has been implemented using C#, which being an object-oriented language, allows for a more efficient, fast and „all axes“ simulation of ground states of solitons in two dimensions. The technique of this method consists in introducing an acceleration operator for each iteration to the imaginary-time equation, which creates the conditions for this method to converge in many solitary waves without nodes.
References
Dauxios, Thierry; Preyrad Michel (2006). Physics of solitons. Cambridge, Inglaterra: Cambridge University Press.
Russel, Scott J. (1844). Report of waves. Proceedings of the Royal Society of Edimburg. 319-320.
Segre, E., editor. (1965). Studies of non linear problems in: collected papers of Enrico Fermi, University of Chicago Press, Vol. II, 978.
Alwyn, C., Scott, F., Chu., Y F., McLaughlin, D. W. (1973). The soliton: a new concept in applied science. Proceedings of the IEEE, 61(10), 1443-1483. https://doi.org/10.1109/PROC.1973.9296
Strecker, K. E. Partridge, G. B. Truscott, A. G., Hulet, F. G. (2002). Nature Formation and propagation of matter-wave soliton trains. Londres, 417, 150. https://doi.org/10.1038/nature747
Yang, J., Lakoba, T. (2008). Accelerated imaginary-time evolutions methods for the computation of solitary waves. Cambridge, EUA. https://doi.org/10.1111/j.1467-9590.2008.00398.x
Malomed, B. A., Mihalache, D., Wise, F., Torner, L. J. (2005). Review article. Spatiotemporal optical solitons. Journal of Optics B, 7, R53-R72. https://doi.org/10.1088/1464-4266/7/5/R02
Lederer, F., Stegeman, G. I., Christodoulides, D. N., Assanto, G., Segev, M, Silberberg, Y. (2008). Spontaneously walking discrete cavity solitons. Phys. Rep. 463, 1. https://doi.org/10.1364/OL.38.001010
Kartashov, Y. V., Malomed, B. A., Torner, L. (2011). Stable bright and vortex solitons in photonic crystal fibers with inhomogeneous defocusing nonlinearity. Rev. Mod. Phys. 83, 247. https://doi.org/10.1364/OL.37.001799
Goldberg, D., Deych, L. I., Lisyansky, A. A., Shi, Z., Menon, V.M., Tokranov, V., Yakimov, M., Oktyabrsky, S. (2009). Dynamical d-wave condensation of exciton -polaritons in a two-dimensional square-lattice potential. Nat. Photon. 3, 662. https://doi.org/10.1038/nphys2012
Kasprzak, J., Richard, M., Kundermann, S., Baas, A., Jeambrun, P., Keeling, J. M. J., Marchetti, F. M., Szymanska, M. H., Andre, R., Staehli, J. L., Savona, V., Littlewood, P. B., Deveaud, B., Dang, L. S. (2006). Nature. Bose-Einstein condensation of exciton polaritons. Londres, 443, 409. https://doi.org/10.1038/nature05131
Liew, T. C. H., Shelykh, I. A., Malpuech, G. (2011). Low-dimensional systems and nanostructures, Physica E 43, 1543.
Baizakov, B. B., Malomed, B. A., Salerno, M. (2004). Multidimensional semi-gap solitons in a periodic potential. Phys. Rev. A 70, 053613. https://doi.org/10.1140/epjd/e2006-00004-8
Mihalache, D., Mazilu, D., Lederer, F., Kartashov, Y. V., Crasovan, L. C., Torner. (2004). Stable three-dimensional spatiotemporal solitons in a two-dimensional photonic lattice, Phys. Rev. E 70, 055603(R). https://doi.org/10.1103/PhysRevE.70.055603
H. L. F. da Luz, F. Kh. Abdullaev, A. Gammal, M. Salerno, L. Tomio. (2010). Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices. Phys. Rev. A 82, 043618. https://doi.org/10.1103/PhysRevA.82.043618
B. A. Malomed. (2006). Soliton Management in Periodic Systems. Nueva York: Springer.
F. Kh. Abdullaev, J. G. Caputo, R. A. Kraenkel, and B. A. Malomed (2003). Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length. Phys. Rev. A 67, 013605. https://doi.org/10.1103/PhysRevA.67.013605
P. G. Kevrekidis, G. Theocharis, D. J. Frantzeskakis, and B. A. Malomed. (2003). Feshbach Resonance Management for Bose-Einstein Condensates. Phys. Rev. Lett. 90, 230401. https://doi.org/10.1103/PhysRevLett.90.230401
M. Matuszewski, E. Infeld, B. A. Malomed, and M. Trippenbach (2005). Fully three dimensional breather solitons can be created using feshbach resonances. Phys. Rev. Lett. 95, 050403. https://doi.org/10.1103/PhysRevLett.95.050403
J. J. G. Ripoll and V. M. Pérez-García. (1999). Barrier resonances in Bose-Einstein condensation. Phys. Rev. A 59, 2220.
I. Towers and B. A. Malomed. (2002). J. Opt. Soc. Am. 19, 537. https://doi.org/10.1103/PhysRevA.59.2220
M. Centurion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis. (2006). Nonlinearity management in optics: experiment, theory, and simulation. Phys. Rev. Lett. 97, 033903. https://doi.org/10.1103/PhysRevLett.97.033903
P. Pedri and L. Santos. (2005). Two-dimensional bright solitons in dipolar bose-einstein condensates. Phys. Rev. Lett. 95, 200404. https://doi.org/10.1103/PhysRevLett.95.200404
D. Briedis, D. E. Petersen, D. Edmundson, W. Krolikowski, and O. Bang. (2005). Ring vortex solitons in nonlocal nonlinear media. Opt. Express 13, 435. https://doi.org/10.1364/OPEX.13.000435
J. Yang and T. I. Lakoba .(2008). Stud. Appl. Math. 120, 265.
G. Burlak, B. A. Malomed. (2012). Matter-wave solitons with a small number of particles in two-dimensional quasiperiodic potentials. Physical Review E, 85, 57601-57606. https://doi.org/10.1103/PhysRevE.85.057601
B. B. Baizakov, B. A. Malomed, and M. Salerno (2004). In nonlinear waves: classical and quantum aspects, edited by F. Kh. Abdullaev and V. V. Konotop. Kluwer Academic, Dordrecht, p. 61.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2013 Programación Mtatemática y Software
This work is licensed under a Creative Commons Attribution 4.0 International License.
Usted es libre de:
Compartir — compartir y redistribuir el material publicado en cualquier medio o formato. |
Adaptar — combinar, transformar y construir sobre el material para cualquier propósito, incluso comercialmente. |
Bajo las siguientes condiciones:
Atribución — Debe otorgar el crédito correspondiente, proporcionar un enlace a la licencia e indicar si se realizaron cambios. Puede hacerlo de cualquier manera razonable, pero de ninguna manera que sugiera que el licenciador lo respalda a usted o a su uso. |
Sin restricciones adicionales: no puede aplicar términos legales o medidas tecnológicas que restrinjan legalmente a otros a hacer cualquier cosa que permita la licencia. |