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Chin. Phys. B, 2020, Vol. 29(9): 090301    DOI: 10.1088/1674-1056/ab928f
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Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials

Ruo-Lin Chai(柴若霖)1, Qiong-Tao Xie(谢琼涛)1, Xiao-Liang Liu(刘小良)2
1 College of Physics and Electronic Engineering, Hainan Normal University, Haikou 571158, China;
2 School of Physics and Electronics, Central South University, Changsha 410083, China
Abstract  The scattering states in one-dimensional Hermitian and non-Hermitian potentials are investigated. An analytical solution for the scattering states is presented in terms of Heun functions. It is shown that for some specially chosen parameter conditions, an infinite number of the exact scattering states is obtained. In the Hermitian potentials, they correspond to the reflectionless states. In the non-Hermitian complex potentials with parity-time symmetry, they are the unidirectionally reflectionless states.
Keywords:  exact solutions      scattering states      non-Hermitian potential  
Received:  12 April 2020      Revised:  05 May 2020      Published:  05 September 2020
PACS:  03.65.Nk (Scattering theory)  
  02.30.Gp (Special functions)  
  42.82.Et (Waveguides, couplers, and arrays)  
Fund: Project supported by the Natural Science Foundation of Hainan Province, China (Grant No. 2019RC179).
Corresponding Authors:  Qiong-Tao Xie     E-mail:  qiongtaoxie@yahoo.com

Cite this article: 

Ruo-Lin Chai(柴若霖), Qiong-Tao Xie(谢琼涛), Xiao-Liang Liu(刘小良) Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials 2020 Chin. Phys. B 29 090301

[1] Szameit A, Dreisow F, Heinrich M, Nolte S and Sukhoruko A A 2011 Phys. Rev. Lett. 106 193903
[2] Heinrich M, Miri M A, Stützer S, Nolte S, Christodoulides D N and Szameit A 2014 Opt. Lett. 39 6130
[3] Longhi S 2015 Opt. Lett. 40 463
[4] Thekkekara L V, Achanta V G and Gupta S D 2014 Opt. Express 22 17382
[5] del Campo A, Boshier M G and Saxena A 2015 Sci. Rep. 4 5274
[6] Bagchi B, Cannata F and Quesne C 2000 Phys. Lett. A 269 79
[7] Huang Y, Veronis G and Min C 2015 Opt. Express 23 29882
[8] Longhi S and Valle G D 2013 Phys. Rev. A 87 052116
[9] Wu N, Zhang C, Jin X R, Zhang Y Q and Lee Y 2018 Opt. Express 26 3839
[10] Wu J H, Artoni M and La Rocca G C 2014 Phys. Rev. Lett. 113 123004
[11] Longhi S 2017 Opt. Lett. 42 3229
[12] Ahmed Z 2001 Phys. Lett. A 282 343
[13] Ahmed Z 2012 J. Phys. A: Math. Theor. 45 032004
[14] Ahmed Z 2013 Phys. Lett. A 377 957
[15] Ghatak A, Mandal R D R and Mandal B P 2013 Ann. Phys. 336 540
[16] Peng B, Ozdemir S K, Lei F, Monifi F, Gianfreda M, Long G L, Fan S, Nori F, Bender C M and Yang L 2014 Nat. Phys. 10 394
[17] Feng L, Xu Y L, Fegadolli W S, Lu M H, Oliveira J E B, Almeida V R, Chen Y F and Scherer A 2013 Nat. Mater. 12 108
[18] Sun Y, Tan W, Li H Q, Li J and Chen H 2014 Phys. Rev. Lett. 112 143903
[19] Eckart C 1930 Phys. Rev. 35 1303
[20] Song J, Hai W and Luo X 2009 Phys. Lett. A 373 1560
[21] Chen B, Wu Y and Xie Q 2013 J. Phys. A: Math. Gen. 46 035301
[22] Agboola D 2014 J. Math. Phys. 55 052102
[23] Panahi H, Baradaran M and Mozhdehi R R 2016 Rom. Rep. Phys. 68 1349
[24] Baradaran M and Panahi H 2017 Adv. High Energy Phys. 2017 2181532
[25] Ronveaux A (ed) 1995 Heun's Differential Equations (Oxford: Oxford University Press) p. 3
[26] Slavyanov S Y and Lay W 2000 Special Functions: A Unified Theory Based on Singularities (Oxford: Oxford University Press) p. 97
[27] Efremov M A, Göbel M C, Hörner Th, Kierig E, Mourachko I and Oberthaler M K 2005 Phys. Rev. Lett. 95 110405
[28] Luo X, Huang J, Zhong H, Qin X, Xie Q, Kivshar Y S and Lee C 2013 Phys. Rev. Lett. 110 243902
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