Geodesic
Edge states and chiral solitons in topological hall and Chern--Simons fields
Modelirovanie i analiz informacionnyh sistem, Tome 25 (2018) no. 1, pp. 133-139.

Voir la notice de l'article provenant de la source Math-Net.Ru

The multi-component extension problem of the $(2+1)D$-gauge topological Jackiw–Pi model describing the nonlinear quantum dynamics of charged particles in multi-layer Hall systems is considered. By applying the dimensional reduction $(2 + 1)D \to (1 + 1)D$ to Lagrangians with the Chern–Simons topologic fields , multi-component nonlinear Schrodinger equations for particles are constructed with allowance for their interaction. With Hirota's method, an exact two-soliton solution is obtained, which is of interest in quantum information transmission systems due to the stability of their propagation. An asymptotic analysis $t\to\pm\infty$ of soliton-soliton interactions shows that there is no backscattering processes. We identify these solutions with the edge (topological protected) states — chiral solitons — in the multi-layer quantum Hall systems. By applying the Hirota bilinear operator algebra and a current theorem, it is shown that, in contrast to the usual vector solitons, the dynamics of new solutions (chiral vector solitons) has exclusively unidirectional motion. The article is published in the author's wording.
Keywords: Chern–Simons fields, topological fields, nonlinear Schrödinger equation, fractional quantum Hall effect.
Mots-clés : chiral solitons 
@article{MAIS_2018_25_1_a12,
     author = {A. M. Agalarov and T. A. Gadzhimuradov and A. A. Potapov and A. E. Rassadin},
     title = {Edge states and chiral solitons in topological hall and {Chern--Simons} fields},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {133--139},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2018_25_1_a12/}
}
TY  - JOUR
AU  - A. M. Agalarov
AU  - T. A. Gadzhimuradov
AU  - A. A. Potapov
AU  - A. E. Rassadin
TI  - Edge states and chiral solitons in topological hall and Chern--Simons fields
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2018
SP  - 133
EP  - 139
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MAIS_2018_25_1_a12/
LA  - en
ID  - MAIS_2018_25_1_a12
ER  - 
%0 Journal Article
%A A. M. Agalarov
%A T. A. Gadzhimuradov
%A A. A. Potapov
%A A. E. Rassadin
%T Edge states and chiral solitons in topological hall and Chern--Simons fields
%J Modelirovanie i analiz informacionnyh sistem
%D 2018
%P 133-139
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MAIS_2018_25_1_a12/
%G en
%F MAIS_2018_25_1_a12
A. M. Agalarov; T. A. Gadzhimuradov; A. A. Potapov; A. E. Rassadin. Edge states and chiral solitons in topological hall and Chern--Simons fields. Modelirovanie i analiz informacionnyh sistem, Tome 25 (2018) no. 1, pp. 133-139. http://geodesic.mathdoc.fr/item/MAIS_2018_25_1_a12/

[1] Lee T.E., “Anomalous Edge State in a Non-Hermitian Lattice”, Phys. Rev. Lett., 116:13 (2016), 133903 | DOI

[2] Leykam D., et. al., “Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems”, Phys. Rev. Lett., 118:4 (2017), 040401 | DOI | MR

[3] Bunkov Yu. M., Volovik G. E., “Magnon Condensation into a $Q$ Ball in $^{3}\mathrm{He}-B$”, Phys. Rev. Lett., 98:26 (2007), 265302 | DOI

[4] Jackiw R., Pi S. Y., “Self-Dual Chern–Simons Solitons”, Prog. Theor. Phys. Suppl., 107 (1992), 1–40 | DOI | MR

[5] Aglietti U., et. al., “Anyons and chiral solitons on a line”, Phys. Rev. Lett., 77:21 (1996), 4406–4409 | DOI

[6] Moon K., et. al., “Spontaneous interlayer coherence in double-layer quantum Hall systems: Charged vortices and Kosterlitz-Thouless phase transitions”, Phys. Rev. B., 51:8 (1995), 5138–5170 | DOI

[7] Agalarov A. M., Magomedmirzaev R. M., “Nontrivial class of composite $U (\sigma+ \mu)$ vector solitons”, JETP Letters, 76:7 (2002), 414–418 | DOI

[8] Novikov S., Manakov S. V., Pitaevskii L. P., Zakharov V. E., Theory of solitons: the inverse scattering method, Springer Science, 1984 | MR

[9] Faddeev L., Jackiw R., “Hamiltonian reduction of unconstrained and constrained systems”, Phys. Rev. Lett., 60:17 (1988), 1692–1694 | DOI | MR

[10] Agalarov A., Zhulego V., Gadzhimuradov T., “Bright, dark, and mixed vector soliton solutions of the general coupled nonlinear Schrödinger equations”, Phys. Rev. E, 91:4 (2015), 042909 | DOI | MR

[11] Hirota R., The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, 2004 | MR

[12] Zakharov V. E., Mikhailov A. V., “Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method”, JETP, 47:6 (1978), 1017–1027 | MR