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Model. Anal. Inform. Sist., 2018, Volume 25, Number 1, Pages 133–139 (Mi mais616)  

Dynamical Systems

Edge states and chiral solitons in topological hall and Chern–Simons fields

A. M. Agalarova, T. A. Gadzhimuradova, A. A. Potapovbc, A. E. Rassadind

a Institute of Physics DSC RAS, 94 M.Yaragsky str., Makhachkala, 367015, Russia
b Kotelnikov Institute of Radioengineering and Electronics (IRE) of Russian Academy of Sciences, 11 Mokhovaya str., buil. 7, Moscow, 125009, Russia
c JNU-IRE RAS Joint Laboratory of Information Technology and Fractal Processing of Signals, JiNan University, 601 Huangpu avenue, Guangzhou, 510632, China
d Nizhny Novgorod Mathematical Society, 23 Gagarin Ave., Nizhny Novgorod, 603950, Russia

Abstract: 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: chiral solitons, Chern–Simons fields, topological fields, nonlinear Schrödinger equation, fractional quantum Hall effect.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-08-01356_а
15-02-03311_а
This work was supported by RFBR, project No 15-02-03311 А. This work was supported by RFBR, project No 18-08-01356-a.


DOI: https://doi.org/10.18255/1818-1015-2018-1-133-139

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UDC: 530.1
Received: 01.12.2017
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Citation: A. M. Agalarov, T. A. Gadzhimuradov, A. A. Potapov, A. E. Rassadin, “Edge states and chiral solitons in topological hall and Chern–Simons fields”, Model. Anal. Inform. Sist., 25:1 (2018), 133–139

Citation in format AMSBIB
\Bibitem{AgaGadPot18}
\by A.~M.~Agalarov, T.~A.~Gadzhimuradov, A.~A.~Potapov, A.~E.~Rassadin
\paper Edge states and chiral solitons in topological hall and Chern--Simons fields
\jour Model. Anal. Inform. Sist.
\yr 2018
\vol 25
\issue 1
\pages 133--139
\mathnet{http://mi.mathnet.ru/mais616}
\crossref{https://doi.org/10.18255/1818-1015-2018-1-133-139}
\elib{http://elibrary.ru/item.asp?id=32482546}


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