Research PaperNo Access

Kinks and realistic impurity models in $φ^{4}$ -theory

Project Management Center of the Southern Research and Educational Center, Don State Technical University, Gagarin square 1, Rostov-on-Don, 344000, Russia

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Jasper Kager

Institute for Theoretical Physics Amsterdam, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands

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Stan de Lange

Institute for Theoretical Physics Amsterdam, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands

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, and

Jasper van Wezel

Institute for Theoretical Physics Amsterdam, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S0217979222500424Cited by:2

Abstract

The $φ^{4}$ -theory is ubiquitous as a low-energy effective description of processes in all fields of physics, ranging from cosmology and particle physics to biophysics and condensed matter theory. The topological defects, or kinks, in this theory describe stable, particle-like excitations. In practice, these excitations will necessarily encounter impurities or imperfections in the background potential as they propagate. Here, we describe the interaction between kinks and various types of realistic impurity models. We find that realistic impurities behave qualitatively like the well-studied, idealized delta function impurities, but that significant quantitative differences appear in both the characteristics of localized impurity modes, and in the collision dynamics. We also identify a particular regime of kink-impurity interactions, in which kinks lose all of their kinetic energy upon colliding with an impurity.

Keywords:

PACS: 11.10.Lm, 11.27.+d, 05.45.Yv, 03.50.−z

References

1. V. L. Ginzburg and L. D. Landau , Zh. Eksp. Teor. Fiz. 20, 1064 (1950). Google Scholar
2. Y. Wada and J. R. Schrieffer , Phys. Rev. B 18, 3897 (1978). Crossref, ISI, ADS, Google Scholar
3. T. Schneider and E. Stoll , Phys. Rev. B 17, 1302 (1978). Crossref, ISI, ADS, Google Scholar
4. S. Aubry , J. Chem. Phys. 64, 3392 (1976). Crossref, ISI, ADS, Google Scholar
5. A. R. Bishop and T. Schneider , Solitons and condensed matter physics, in Proc. Symp. Nonlinear (Soliton) Structure and Dynamics in Condensed Matter (Oxford, 1978), pp. 195–198. Crossref, Google Scholar
6. A. R. Bishop , Solid State Commun. 33, 955 (1980). Crossref, ISI, ADS, Google Scholar
7. M. J. Rice and E. J. Mele , Solid State Commun. 35, 487 (1980). Crossref, ISI, ADS, Google Scholar
8. A. Friedland, H. Murayama and M. Perelstein , Phys. Rev. D 67, 043519 (2003). Crossref, ISI, ADS, Google Scholar
9. D. K. Campbell and Y.-T. Liao , Phys. Rev. D 14, 2093 (1976). Crossref, ISI, ADS, Google Scholar
10. T. D. Lee and G. C. Wick , Phys. Rev. D 9, 2291 (1974). Crossref, ISI, ADS, Google Scholar
11. J. Boguta , Phys. Lett. B 128, 19 (1983). Crossref, ISI, ADS, Google Scholar
12. S. Hu, M. Lundgren and A. J. Niemi , Phys. Rev. E 83, 061908 (2011). Crossref, ADS, Google Scholar
13. A. Molochkov, A. Begun and A. Niemi , EPJ Web Conf. 137, 04004 (2017). Crossref, Google Scholar
14. S. Hu et al., Phys. Rev. E 83, 041907 (2011). Crossref, ADS, Google Scholar
15. T. I. Belova and A. E. Kudryavtsev, Usp. Fiz. Nauk 167, 377 (1997) [Sov. Phys. Usp. 40, 359 (1997)]. Google Scholar
16. D. K. Campbell , Historical overview of the Phi-Fourth model, in A Dynamical Perspective on the Phi-Fourth Model: Past, Present, and Future, eds. P. G. KevrekidisJ. Cuevas-Maraver (Springer, 2019), pp. 1–22. Crossref, Google Scholar
17. M. J. Ablowitz, M. D. Kruskal and J. F. Ladik , SIAM J. Appl. Math. 36, 428 (1979). Crossref, ISI, ADS, Google Scholar
18. P. Anninos, S. Oliveira and R. A. Matzner , Phys. Rev. D 44, 1147 (1991). Crossref, ISI, ADS, Google Scholar
19. R. Goodman and R. Haberman , SIAM J. Appl. Dyn. Syst. 4, 1195 (2005). Crossref, ISI, ADS, Google Scholar
20. V. A. Gani, A. E. Kudryavtsev and M. A. Lizunova , Phys. Rev. D 89, 125009 (2014). Crossref, ISI, ADS, Google Scholar
21. V. A. Gani, V. Lensky and M. A. Lizunova , J. High Energy Phys. 8, 147 (2015). Crossref, ISI, Google Scholar
22. P. Dorey et al., J. High Energy Phys. 2021, 145 (2021). Crossref, Google Scholar
23. D. Bazeia, A. R. Gomes and F. C. Simas , Eur. Phys. J. C 81, 532 (2021). Crossref, ISI, ADS, Google Scholar
24. I. C. Christov et al., Commun. Nonlinear Sci. Numer. Simul. 97, 105748 (2021). Crossref, ISI, Google Scholar
25. D. Bazeia et al., Int. J. Mod. Phys. A 34, 1950200 (2019). Link, ADS, Google Scholar
26. V. A. Gani, A. M. Marjaneh and D. Saadatmand , Eur. Phys. J. C 79, 620 (2019). Crossref, ISI, ADS, Google Scholar
27. V. A. Gani et al., Eur. Phys. J. C 78, 345 (2018). Crossref, ISI, ADS, Google Scholar
28. Z. Fei, Y. S. Kivshar and L. Vazquez , Phys. Rev. A 46, 5214 (1992). Crossref, ISI, ADS, Google Scholar
29. Z. Fei et al., Phys. Rev. E 48, 548 (1993). Crossref, ISI, ADS, Google Scholar
30. K. Javidan , J. Phys. A: Math. Gen. 39, 10565 (2006). Crossref, ADS, Google Scholar
31. E. Hakimi and K. Javidan , Phys. Rev. E 80, 016606 (2009). Crossref, ADS, Google Scholar
32. A. Ghahraman and K. Javidan , Braz. J. Phys. 41, 171 (2011). Crossref, ISI, ADS, Google Scholar
33. K. Javidan , Phys. Rev. E 78, 046607 (2008). Crossref, ADS, Google Scholar
34. A. Askari, D. Saadatmand and K. Javidan , Waves Random Complex Media 29, 368 (2018). Crossref, ISI, Google Scholar
35. D. Bazeia , in Proc. XIII J. A. Swieca Summer School on Particles and Fields (SP, 2005). Google Scholar
36. R. Rajaraman , Phys. Rep. C 21, 227 (1975). Crossref, ADS, Google Scholar
37. E. B. Bogomolny, Yad. Fiz. 24, 861 (1976) [Sov. J. Nucl. Phys. 24, 449 (1976)]. Google Scholar
38. M. K. Prasad and C. M. Sommerfield , Phys. Rev. Lett. 35, 760 (1975). Crossref, ISI, ADS, Google Scholar
39. D. K. Campbell, J. S. Schonfeld and C. A. Wingate , Phys. D 9, 1 (1983). Crossref, ISI, ADS, Google Scholar
40. A. E. Kudryavtsev and M. A. Lizunova , Phys. Rev. D 95, 056009 (2017). Crossref, ADS, Google Scholar

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Vol. 36, No. 05

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History

Received 7 October 2021

Revised 20 December 2021

Accepted 27 December 2021

Published: 22 February 2022

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Kinks and realistic impurity models in φ4-theory

Abstract

References

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Kinks and realistic impurity models in $φ^{4}$ -theory