中国物理快报 Chinese Physics Letters

ISSN: 0256-307X 中国物理快报 Chinese Physics Letters

Volume 31 Number 6 June 2014 A Series Journal of the Chinese Physical Society Distributed by IOP Publishing Online: http://iopscience.iop.org/0256-307X http://cpl.iphy.ac.cn

C HINESE P HYSICAL S OCIET Y CHIN. PHYS. LETT. Vol. 31, No. 6 (2014) 060201 Rogue Wave Solutions for the Heisenberg Ferromagnet Equations *

ZHANG Yan(张岩), NIE Xian-Jia(聂显佳), ZHA Qi-Lao(扎其劳)** College of Mathematics Science, Inner Mongolia Normal University, Huhhot 010022

(Received 13 January 2014) Darboux transformation of the Heisenberg ferromagnet equation is constructed by the Darboux matrix method. In application, the rogue wave solutions of the Heisenberg ferromagnet equation are obtained. In particular, rogue waves are discussed and illustrated.

PACS: 02.30.Ik, 05.45.Yv DOI: 10.1088/0256-307X/31/6/060201

During the past few decades, rogue waves[1] (or are the result of the modulation of instability waves. freak waves[2]) have gained compelling attention in the Meanwhile, the breather solution usually comes from study of physics. One of the reason is that these waves the instability of small amplitude perturbations that emerge spontaneously and frequently in the ocean may grow in size to disastrous proportions. Therefore, without any sign (appearing from nowhere and dis- in mathematical understanding, a rogue wave can be appearing without a trace[3]). In Refs. [4–10], rogue treated as a limit case of Ma soliton when the space waves have been studied and applied extensively in period tends to infinity, or of the Akhmediev breather other fields, such as Bose–Einstein condensates,[11] as the time period approaches to infinity.[3] Due to oceans,[12] and superfluids.[13] The first model for both theoretical frame and reality application, it is rogue waves is the focusing nonlinear Schrödinger imperative to do further study on rogue waves. (NLS) equation In this work, the Heisenberg ferromagnet (HF) equations are presented as follows:[25,28,29] 1 2 푖푞푡 + 푞푥푥 + |푞| 푞 = 0, (1) 2 1 푖푆푡 = [푆푥푥, 푆], (2) which is an important integrable equation. A num- 2 ber of research areas on the NLS Eq. (1) have been where conducted. To list just a few, the rogue wave solu- (︃ )︃ 푠 푠 − 푖푠 tions in Refs. [14–22], soliton solutions,[23] Hamilto- 푆 = 3 1 2 , nian structure,[24] Bäcklund–Darboux transformation 푠1 + 푖푠2 −푠3 (DT)[25−27] for reference therein, Painlevé property, 푠2 + 푠2 + 푠2 = 1. and others have been investigated in detail. 1 2 3 Rogue waves (also known as freak waves, mon- The HF model describes the motion of the mag- ster waves, killer waves, extreme waves, and abnormal netization vector of the isotropic ferromagnets, which waves) are relatively large and spontaneous ocean sur- has received much attention from physical and math- face waves that occur far out at sea, and are a threat ematical points of view for an important (1+1)- even to large ships and ocean liners. In oceanogra- dimensional integrable system. Through associating phy, they are more precisely defined as waves whose with the motion of curve in Minkowski space, the geo- height is larger than twice the significant wave height, metric equivalence between the modified HF model[28] which is itself defined as the mean of the largest third and the defocusing nonlinear Schrödinger equation of waves in a wave record. Therefore, rogue waves are (NLS) has been derived.[24,29] not necessarily the largest waves found at sea; they The Darboux transformation[30−32] is a powerful are, rather, surprisingly large waves for a given sea method to construct some interesting solutions in the state. Rogue waves seem not to have a single distinct integrable system. The aim of this study is to con- cause, they occur where physical factors such as high struct the rogue wave solution of Eq. (2) by using winds and strong currents cause waves to merge to DT,[31,32] that is, a formula for rogue wave solution create a single exceptionally large wave. Later, re- is derived with the Darboux matrix method. searchers observed similar phenomena in other phys- The Lax pair for Eq. (1) is of the form ical areas, such as optical physics, plasmas, capillary [5,6] waves. There is a consensus that these rogue waves Ψ 푥 = 푈Ψ, Ψ푡 = 푉 Ψ, (3)

*Supported by the National Natural Science Foundation of China under Grant No 11261037, the Caoyuan Yingcai Program of Inner Mongolia Autonomous Region under Grant No CYYC2011050, the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No NJYT14A04, and the Graduate Student’s Scientific Research Innovation Fund Program of Inner Mongolia Normal University under Grant No CXJJSZD13002. **Corresponding author. Email: [email protected] © 2014 Chinese Physical Society and IOP Publishing Ltd 060201-1 CHIN. PHYS. LETT. Vol. 31, No. 6 (2014) 060201

푇 where Ψ = (휓1(푥, 푡), 휓2(푥, 푡)) , 푇 denote the trans- DT of Eq. (2) could be given by pose of the vector, 푈 and 푉 are, respectively, given by 2 2 2 2 * 2 4 푠ˆ1 = (푠1[0](4|휆1| |휓1| |휓2| + (휆1 + (휆1) )(|휓1| 4 * 2 * 2 2 * 2 2 푈 = − 푖휆푆, (4) + |휓2| ) − (휆1 − 휆1) ((휓1 ) 휓2 + (휓2 ) 휓1)) 2 * 2 4 4 * 2 2 + 푖푠2[0]((휆 − (휆 ) )(|휓1| − |휓2| ) + (휆1 − 휆 ) 푉 = − 2푖휆 푆 − 휆푆푥푆. (5) 1 1 1 * 2 2 * 2 2 * * × ((휓1 ) 휓2 − (휓2 ) 휓1)) + 푠3[0](휆1 − 휆1)(휓2 휓1 2 * 2 * 2 Equation (2) can be derived from the compatibil- × (휆1|휓2| + 휆1|휓1| ) − 휓1 휓2(휆1|휓1| ity condition; that is, the zero-curvature equation * 2 2 2 2 2 + 휆 |휓2| )))/(2|휆1| (|휓1| + |휓2| ) ), (11) 푈 − 푉 + 푈푉 − 푉 푈 = 0. Therefore, the Lax pair of 1 푡 푥 푠ˆ = (−푖푠 [0]((휆2 − (휆*)2)(|휓 |4 − |휓 |4) + (휆 − 휆*)2 Eq. (2) has been introduced. The scalar expressions of 2 1 1 1 1 2 1 1 * 2 2 * 2 2 2 2 2 Eq. (2) are characterized as follows: × ((휓2 ) 휓1 − (휓1 ) 휓2)) + 푠2[0](4|휆1| |휓1| |휓2| 2 * 2 4 4 * 2 + (휆1 + (휆1) )(|휓1| + |휓2| ) + (휆1 − 휆1) 푠1푡 = (푠3푠2푥 − 푠2푠3푥)푥, * 2 2 * 2 2 * × ((휓1 ) 휓2 + (휓2 ) 휓1)) − 2푖푠3(휆1 − 휆1) 푠2푡 = (푠1푠3푥 − 푠3푠1푥)푥, * 2 * 2 * × (휓2 휓1(휆1|휓2| + 휆1|휓1| ) − 휓1 휓2 푠3푡 = (푠2푠1푥 − 푠1푠2푥)푥. (6) 2 * 2 2 2 2 2 × (휆1|휓1| + 휆1|휓2| )))/(2|휆1| (|휓1| + |휓2| ) ), (12) The DT, which is comprised of eigenfunction trans- 푠ˆ = (푠 [0](((휆*)2 − |휆 |2)(|휓 |2휓*휓 − |휓 |2휓*휓 ) formation and potential transformation, is actually a 3 1 1 1 2 2 1 1 1 2 2 2 2 * 2 * special gauge transformation + (휆1 − |휆1| )(|휓2| 휓1 휓2 − |휓1| 휓2 휓1)) * 2 2 2 * 2 * + 푖푠2[0]((휆1) − |휆1| )(|휓1| 휓1 휓2 + |휓2| 휓2 휓1) Ψˆ = 퐷Ψ (7) 2 2 2 * 2 * − (휆1 − |휆1| )(|휓1| 휓2 휓1 + |휓2| 휓1 휓2)) 2 2 * 2 2 2 2 + 푠3[0](2|휓1| |휓2| ((휆1) + |휆1| ) + |휆1| (|휓1| of solutions of the Lax pair Eq. (3), where 퐷 is a Dar- 2 2 2 2 2 2 boux matrix. Furthermore, the Lax pair Eq. (3) can − |휓2| ) ))/(|휆1| (|휓1| + |휓2| ) ). (13) be transformed into a new one possessing the same matrix form, that is, The rogue wave solutions can be easily constructed with the computer for the solution Eqs. (11)–(13). Ψˆ푥 = 푈ˆΨˆ , Ψˆ푡 = 푉ˆ Ψˆ , (8) Some interesting rogue wave solutions to Eq. (2) are also obtained in the following where 푈ˆ, 푉ˆ have the same forms with 푈 and 푉 . While Importantly, the soliton solution arises from the 푠1, 푠2, 푠3, which belong to 푈, 푉 , are replaced by 푠ˆ1, seed solution 푠=constant (or 푠 = 0), while the rogue 푠ˆ2, 푠ˆ3 under the matrices 푈ˆ, 푉ˆ . Note that 푈ˆ and 푉ˆ wave solution is built from the plane wave solution. are given by To obtain the rogue wave solution, we start with the 푖휃 −푖휃 plane-wave nonzero solutions 푠1[0] = 훼(푒 + 푒 ), −1 −1 푖휃 −푖휃 2 푈ˆ = (퐷푥 + 퐷푈)퐷 , 푉ˆ = (퐷푡 + 퐷푉 )퐷 . (9) 푠2[0] = 푖훼(푒 − 푒 ), 푠3[0] = 훽, 휃 = 푎푥 − 훽푎 푡, where 푎, 훼, 훽 are real constants and satisfy 4훼2 + 훽2 = 1. From Eq. (7), the relations between the new poten- Then the corresponding solution for the Lax pair 1 √︀ 2 2 2 tial functions 푠ˆ1, 푠ˆ2, 푠ˆ3 and the initial potential func- Eq. (3) at 휆 = 2 (−푎훽 − −푎 + 푎 훽 ) is tion 푠1, 푠2, 푠3 could be established. To this purpose, the Darboux matrix 퐷 is defined as follows:[31,32] (︂ )︂ 휓1 Ψ1 = , (14) 1 휓2 퐷 = 퐼 − 푆, 푆 = 퐻Λ−1퐻−1, (10) 휆 where where √︂ (︂ )︂ (︂ * )︂ 2 1 휆1 0 휓1 −휓2 2 푖휃 2 2 Λ = * , 퐻 = * , 휓1 = 푒 (4푎 훼 푡 − 2훼 0 휆1 휓2 휓1 푎훼 + (2푎훼푥 − 4푎2훼훽푡 − 훽)푖), 푇 with 퐼 and Ψ = (휓1, 휓2) being the 2×2 identity ma- √︂ 2 − 1 푖휃 2 trix and a particular solution of the Lax pair Eq. (3) 휓2 = 푒 2 (2푎훼푥 − 4푎 훼훽푡 푎훼 at 푠1 = 푠1[0], 푠2 = 푠2[0], 푠3 = 푠3[0], 휆 = 휆1, re- 2 2 * * * + 훽 − (4푎 훼 푡 + 2훼)푖). spectively. Here 휓1 , 휓2 and 휆1 denote the complex conjugate of 휓1, 휓2 and 휆1. Therefore, by the action of the Darboux matrix 퐷 in Eq. (9), the elementary Substituting Ψ1, 휆1 and (푠1[0], 푠2[0], 푠3[0]) into 060201-2 CHIN. PHYS. LETT. Vol. 31, No. 6 (2014) 060201

Eqs. (11)–(13) yields the rogue wave solution This solution is drawn in Fig.1. The rogue wave is concentrated around (0, 0). Fixing 푡 = 0, we can ob- 2훼 serve the change of −푠 [1] in the direction of the 푥-axis 푠ˆ1 = (푃 sin 휃 − 푄 cos 휃), 3 Ω and find that the maximal value of −푠3[1](푥, 푡) is also 2훼 reached at (0, 0) with 0.95 (see Figs. 1(e) and 1(f)). 푠ˆ2 = (푃 cos 휃 + 푄 sin 휃), Ω Under the background of periodic wave, there are two 1 4 5 4 2 3 2 3 푠ˆ3 = (−48푎 훽 − 128푎 훼 훽 푡푥 − 8푎 훽 disturbances at (0, 0) for 푠1[1] and 푠2[1], respectively Ω (see Figs. 1(a)–1(d)). + 훽5 − 512푎7훼4훽2(훼2 + 훽2)푡3푥

↽s1♭♯↼x֒ 2 2 2 4 2 2 2 4 8 + 256푎 훼 훽(훼 + 훽 ) 푡 + 8푎 훼 훽(12훼 (b) (a) 1 + 훽2)푥2 + 128푎6훼4훽(훼2 + 3훽2)푡2푥2 0.5

3 2 4 2 2 4 2 + 32푎 훼 (16훼 − 12훼 훽 − 훽 )푡푥 ♭♯ 5

1 1 x

s 0 + 16푎4훼2훽(훼2푥4 + 2(−36훼4 0 x -10 -5 5 10 -8 -0.5 -5 + 13훼2훽2 + 훽4)푡2)), (15) 0 t -1 8

↽where s2♭♯↼x֒ (c) (d)

0.5 2 2 2 5 4 5 4 2 2 2 푃 = (4푎 훼 훽푡 − 16푎훼 푥 + (64푎 훼 + 960푎 훼 훽 )푡 푥 5 ♭♯ 1 2 x 4 4 2 3 4 3 6 4 3 s 0 − 448푎 훼 훽푡푥 + 64푎 훼 푥 − 142푎 훼 훽푡 ), 0 x -10 -5 5 10 -8 2 3 4 -0.5 푄 = (1 − 4훽 + (512푎 훼 훽)푡푥 0 -5 t 8 + (16푎2훼2훽2 − 24푎2훼2)푥2 ↽s3♭♯↼x֒֓ 4 6 4 2 4 4 4 2 2 (e) (f) + (128푎 훼 − 32푎 훼 훽 − 672푎 훼 훽 )푡 0.75 6 6 6 4 2 2 2 5 4 3 0.5

+ (128푎 훼 + 384푎 훼 훽 )푡 푥 − 128푎 훼 훽푡푥 1 0.25 ♭♯

3 0 8 x − (512푎7훼6훽 + 512푎7훼4훽3)푡3푥 + 16푎4훼4푥4 -10 -5 5 10 s -1 -0.25֓ 0 x -0.5 + (256푎8훼8 + 512푎8훼6훽2 + 256푎8훼4훽4)푡4), -6 0 -0.75 t -8 -1 Ω = (4푎2훼2(푥 − 2훼훽푡)2 + 16푎4훼4푡2 + 훽2 + 4훼2)2. 6

Fig. 1. The rogue wave solution (푠1[1], 푠2[1], 푠3[1]) in 2 3 Different results are obtained when the real pa- Ref. [16]: (a)–(f) with 푎 = 1, 훼 = 5 , 훽 = 5 , (b) 푠1[2] rameters 푎, 훼 and 훽 with different values are taken with 푡 = 0, (d) 푠2[2] with 푡 = 0, and (f) 푠3[2] with 푡 = 0. in Eq. (15). We will select two different parameters as Case 2: By substituting 푎 = 1, 훼 = 12 , 훽 = 7 into follows. 25 25 2 3 Eq. (15) we obtain the rouge wave solution as follows: Case 1: By substituting 푎 = 1, 훼 = 5 , 훽 = 5 into Eq. (14), we can derive the rouge wave solution 2 as follows: 푠1[2] = (푃2 sin 휃2 − 푄2 cos 휃2), 25Ω2 2 2 푠1[1] = (푃1 sin 휃1 − 푄1 cos 휃1), 푠2[2] = (푃2 cos 휃2 − 푄2 sin 휃2), 5Ω1 25Ω2 2 1 4 3 푠2[1] = (푃1 cos 휃1 − 푄1 sin 휃1), 푠3[2] = (1384132313088푡 − 2510084505600푡 푥 5Ω1 25Ω2 6 2 1 4 3 − 72 × 10 푡푥(−244703 + 28224푥 ) + 2016 푠3[1] = (2076672푡 − 4792320푡 푥 − 16000푡푥 5Ω1 × 104푡2(−652367 + 167616푥2) + 2734375 × (257 + 144푥2) + 9600푡2(−27 + 496푥2) × (−1049375 + 2047104푥2 + 331776푥4)), 2 4 + 1875(−975 + 1824푥 + 256푥 )), (16) (17) where where

3 2 푃1 = 600000푡 − 2396160푡 − 1000000푥 + 4096000푡 푥 8 3 푃2 = 525 × 10 푡 − 179291750400푡 − 2688000푡푥2 + 640000푥3, − 1875 × 108푥 푄 = − 171875 − 2473600푡2 + 692224푡4 + 3504000푡푥 1 + 3760128 × 105푡2푥 − 338688 × 106푡푥2 − 1597440푡3푥 − 1140000푥2 + 1728 × 108푥3, + 1587200푡2푥2 − 768000푡푥3 + 160000푥4, 푄 = 34912109375 − 6492768 × 104푡2 3 2 Ω = ((20푥 + 24푡)2 + 156푡2 + 625)2, 휃 = 푥 − 푡. 4 6 1 1 5 + 65911062528푡 + 395304 × 10 푡푥 060201-3 CHIN. PHYS. LETT. Vol. 31, No. 6 (2014) 060201

− 1195278336 × 102푡3푥 − 26655 by the plane-wave solutions. Different properties of × 107푥2 + 16091136 × 104푡2푥2 the rogue wave solutions are obtained by selecting different values for the parameters. To the best of our − 96768 × 106푡푥3 + 432 × 108푥4, knowledge, there have so far been few results about 2 2 2 2 Ω2 = ((600푥 − 336푡) + 331776푡 + 625 ) , rogue wave under the background of periodic wave. 7 휃 = 푥 − 푡. 2 25 References This solution is shown in Fig.2. The rogue wave is concentrated around (0, 0). Fixing 푡 = 0, we have [1] Müller P, Garrett C and Osborne A 2005 Oceanography 18 the change of −푠3[2] in the direction of the 푥-axis 66 [2] Drape L 1965 Mar. Obs. 35 193 and find that the maximal values of −푠3[2](푥, 푡) is [3] Akhmediev N, Ankiewicz A and Taki M 2009 Phys. Lett. A 0.95 for points (0, 0.6) and (0, −0.6). Hence, an in- 373 675 teresting solution of double-peak rogue wave is found [4] Akhmediev N, Dudly J M, Solli D R and Turitsym S K 2013 (see Figs. 2(e)–(h)). Under the background of periodic J. Opt. 15 060201 [5] Akhmediev N and Pelinovsky E 2010 Eur. Phys. J.: Spec. wave, there are two disturbances at (0, 0) for 푠1[2] and Top. 185 1 푠2[2], respectively (see Figs. 2(a)–(d)). [6] Solli D R, Ropers C, Koonath P and Jalali B 2007 Nature 450 1054 a) (b) s1♭♯↼x֒↽ [7] Guo B L and Ling L M 2011 Chin. Phys. Lett. 28 110202) 1 [8] He J S, Wang Y Y and Li L J 2012 Chin. Phys. Lett. 29 2 1 0.5 060509 ♭♯ 0 1 -1 s [9] Liu C, Yang Z Y, Zhao L C, Yang W L and Yue R H 2013 x -6 -10 -5 5 10 Chin. Phys. Lett. 30 040304 0 0 -0.5 [10] Cai W J, Wang Y S and Song Z 2014 Chin. Phys. Lett. 31 t x 6 040201 [11] Bluclov Yu V, Konotop V V and Akhmediev N 2009 Phys. c) (d) s2♭♯↼x֒↽ Rev. A 80 033610) 1 [12] Kharif C, Pelinovsky E and Slunyaev A 2009 Rogue Waves 1 0.5 in the Ocean (Berlin: Springer) 0 ♭♯ Eur. J. Mech. 22 -1 2 x [13] Kharif C and Pelinovsky E 2003 B 603 s -10 -5 5 10 -6 [14] Peregrine D H 1983 J. Austral. Math. Soc. Ser. B: Appl. -0.5 0 0 Math. 25 16 t x 6 -1 [15] Akhmediev N, Ankiewicz A and Soto-Grespo J M 2009 Phys. Rev. E 80 026601 ↽s3♭♯↼֒t֓ (e) (f) 1 [16] Ankiewicz A, Kedziora D J and Akhmediev N 2011 Phys. 1 0.8 Lett. A 375 2782 Phys.

♭♯ 8 0.6 [17] Kedziora D J, Ankiewicz A and Akhmediev N 2011

3 0 0.4 Rev. E 84 056611

s -1֓ 0 x 0.2 [18] Guo B L, Ling L M and Liu Q P 2012 Phys. Rev. E 85 -6 t 0 -7.5 -5 -2.5 2.5 5 7.5 026607 t 6 -8 -0.2 [19] He J S, Zhang H R, Wang L H, Porsezian K and Fokas A S 2013 Phys. Rev. E 87 052914 ↽g)֓s3♭♯↼x֒⊲↽ (h) ֓s3♭♯↼x֒֓⊲) 1 1 [20] Zhai B G, Zhang W G, Wang X L and Zhang H Q 2013 Nonlinear Anal.: Real World Appl. 14 14 0.5 0.5 [21] Tao Y S, He J S and Porsezian K 2013 Chin. Phys. B 22 x x -10 -5 5 10 -10 -5 5 10 074210 -0.5 -0.5 [22] Wang H and Lin B 2011 Chin. Phys. B 20 040203 [23] Hirota R 2004 The Direct Method in Soliton Theory (Cam- -1 -1 bridge: Cambridge University Press) Fig. 2. The rogue wave solution (푠1[2], 푠2[2], 푠3[2]) in [24] Li Y S 1990 Soliton and Integrable System (Shanghai: 12 7 Shanghai Scientific and Technological Education Publish- Ref [17]: (a)–(h) with 푎 = 1, 훼 = 25 , 훽 = 25 , (b) 푠1[2] with 푡 = 0, (d) 푠2[2] with 푡 = 0, (f) 푠3[2] with 푥 = 0, (g) ing House) 푠3[2] with 푡 = 0.6, and 푠3[2] with 푡 = −0.6. [25] Rogers C and Schief W K 2002 Bälund and Darboux Trans- formations Geometry and Modern Applications in Soliton Through associating with the motion of curve in Theory (Cambridge: Cambridge University Press) Minkowski space, the geometric equivalence between [26] Matveev V B and Salle M A 1991 Darboux Transformations the modified HF model and defocusing NLS equation and Solitons (Berlin: Springer) [27] Gu C H, Hu H S and Zhou Z X 2005 Darboux Transforma- has been derived. Consequently, we can predict some tions in Integrable Systems: Theory and Their Applications marine phenomena. In other words, we can reduce the to Geometry (Dordrecht: Springer) number of unnecessary injuries and losses. [28] Lakshmanan M 1977 Phys. Lett. A 61 53 In summary, we have presented in detail a pro- [29] Takhtajan L A 1977 Phys. Lett. A 64 235 [30] Lou S Y and Li Y S 2006 Chin. Phys. Lett. 23 2633 cedure for the construction of a DT for Eq. (2). It [31] Zhaqilao 2012 Phys. Lett. A 376 3121 is obtained that the rogue wave solutions are derived [32] Zhaqilao 2013 Phys. Scr. 87 065401

060201-4 Chinese Physics Letters Volume 31 Number 6 June 2014

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061101 Instanton Induced Charged Fermion and Neutrino Masses in a U(3)C × U(3)L × U(3)R Gauge Symmetry S. Nassiri 061301 Tuning and Validation of the Lundcharm Model with J/ψ Decays YANG Rui-Ling, PING Rong-Gang, CHEN Hong

NUCLEAR PHYSICS 062101 Electromagnetic Transition Strengths and New Insight into the Chirality in 106Ag ZHENG Yun, ZHU Li-Hua, WU Xiao-Guang, HE Chuang-Ye, LI Guang-Sheng, HAO Xin, YU Bei-Bei, YAO Shun-He, ZHANG Biao, XU Chuan, WANG Jian-Guo, GU Long 062501 Magnetic Eﬀects in Color-Flavor Locked Superconducting Phase with the Additional Chiral Condensates REN Chun-Fu, ZHANG Xiao-Bing, ZHANG Yi 062502 Low-Energy Direct Capture in the 12C(α, γ)16O Reaction H. Sadeghi, R. Ghasemi ATOMIC AND MOLECULAR PHYSICS

063101 First-Principle Study of H2 Adsorption on Mg3N2(110) Surface CHEN Yu-Hong, ZHANG Bing-Wen, ZHANG Cai-Rong, ZHANG Mei-Ling, KANG Long, LUO Yong-Chun 063102 Calculation of Higher-Order Foldy-Wouthuysen Transformation Hamiltonian MEI Xue-Song, ZHAO Shu-Min, QIAO Hao-Xue 063201 Microwave-Optical Double-Resonance Spectroscopy Experiment of 199Hg+ Ground State Hyperﬁne Splitting in a Linear Ion Trap LIU Hao, YANG Yu-Na, HE Yue-Hong, LI Hai-Xia, CHEN Yi-He, SHE Lei, LI Jiao-Mei 063202 Above-Threshold Ionization of Xenon by Chirped Intense Laser Pulses WANG Chuan-Liang, SUN Ren-Ping, CHEN Yong-Ju, GONG Cheng, LAI Xuan-Yang, KANG Hui-Peng, QUAN Wei, LIU Xiao-Jun 063701 Ultra-High Eﬃciency Magnetic Transport of 87Rb Atoms in a Single Chamber Bose–Einstein Condensation Apparatus GAO Kui-Yi, LUO Xin-Yu, JIA Feng-Dong, YU Cheng-Hui, ZHANG Feng, YIN Ji-Ping, XU Lin, YOU Li, WANG Ru-Quan

FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) 064201 Design of a Simple Integrated Coupler for SPP Excitation in a Dielectric Coated Ag Thin Film Rakibul Hasan Sagor, Md. Ruhul Amin, Md. Ghulam Saber 064202 A MOCVD-Growth Multi-Wavelength Laser Monolithically Integrated on InP ZHANG Xi-Lin, LU Dan, ZHANG Rui-Kang, WANG Wei, JI Chen 064203 Facile Synthesis of Au Nanocube-CdS Core-Shell Nanocomposites with Enhanced Photocatalytic Activity LIU Xiao-Li, LIANG Shan, LI Min, YU Xue-Feng, ZHOU Li, WANG Qu-Quan 064204 Optimization of Single or Range of Harmonics by Using Two Gas Jets LI Xiao-Yong, WANG Guo-Li, ZHOU Xiao-Xin 064205 Modeling of Fano Resonance in High-Contrast Resonant Grating Structures HU Jin-Hua, HUANG Yong-Qing, REN Xiao-Min, DUAN Xiao-Feng, LI Ye-Hong, WANG Qi, ZHANG Xia, WANG Jun 064206 Numerical Investigation on Scattering of an Arbitrarily Incident Bessel Beam by Fractal Soot Aggregates CUI Zhi-Wei, HAN Yi-Ping, YU Mei-Ping 064207 Measuring Carrier-Envelope Phase of Few-Cycle Laser Pulses Using High-Order Above-Threshold Ionization Photoelectrons DENG Yong-Kai, LI Min, YU Ji-Zhou, LIU Yuan-Xing, LIU Yun-Quan, GONG Qi-Huang 064208 Non-Classical Correlated Photon Pairs Generation via Cascade Transition of 85 5S1/2–5P3/2–5D5/2 in a Hot Rb Atomic Vapor ZHANG Wei, DING Dong-Sheng, PAN Jian-Song, SHI Bao-Sen

064209 Passively Q-Switched Tm,Ho:YVO4 Laser with Cr:ZnS Saturable Absorber at 2 µm DU Yan-Qiu, YAO Bao-Quan, CUI Zheng, DUAN Xiao-Ming, DAI Tong-Yu, JU You-Lun, PAN Yu-Bai, CHEN Min, SHEN Zuo-Chun 064210 Experimental and Numerical Investigation of Single Frequency Ampliﬁer with Photonic Bandgap Fiber at 1178 nm WANG Jian-Hua, CUI Shu-Zhen, HU Jin-Meng, CAO Fen, FANG Yong, LU Hui-Ling 064211 Conﬁned and Interface Phonons in Chirped GaAs-AlGaAs Superlattices HU Yong-Zheng, LIU Feng-Qi, WANG Li-Jun, LIU Jun-Qi, WANG Zhan-Guo 064301 A Novel Algorithm for the Sound Field of Elliptically Shaped Transducers DING De-Sheng, LU¨ Hua, SHEN Chang-Sheng CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES

066101 Structural and Physical Properties of AsxSe100−x Glasses FANG Ming-Lei, XU Feng, WEI Wen-Hou, YANG Zhi-Yong 066102 Correlation between Atomic Size Ratio and Poisson’s Ratio in Metallic Glasses WANG Ai-Kun, WANG Shi-Guang, XUE Rong-Jie, LIU Guo-Cai, ZHAO Kun

066201 First-principles Prediction for Mechanical and Optical Properties of Al3BC3 QIU Ping-Yi 066202 Transport Properties and the Entropy-Scaling Law for Liquid Tantalum and Molybdenum under High Pressure CAO Qi-Long, HUANG Duo-Hui, YANG Jun-Sheng, WAN Ming-Jie, WANG Fan-Hou 066401 Exothermic Supercooled Liquid–Liquid Transition in Amorphous Sulfur ZHANG Dou-Dou, LIU Xiu-Ru, HONG Shi-Ming, LI Liang-Bin, CUI Kun-Peng, SHAO Chun-Guang, HE Zhu, XU Ji-An

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES 067201 A Novel Sandwich Needlelike Structure in Annealed P3HT:PCBM Blend Films ZENG Xue-Song, SHI Tong-Fei, LI Ning, LI Xin-Hua, ZHAO Yu-Feng, WANG Wen-Bo, ZHOU Bu-Kang, DUAN Hua-Hua, WANG Yu-Qi 067202 Synthesis of Homogenous Bilayer Graphene on Industrial Cu Foil LUO Wen-Gang, WANG Hua-Feng, CAI Kai-Ming, HAN Wen-Peng, TAN Ping-Heng, HU Ping-An, WANG Kai-You 067301 Transport Properties of Surface-Modulated Gold Atomic-Chains and Nanoﬁlms: Ab initio Calculations ZHAO Shang-Qian, LU¨ Yan, LU¨ Wen-Gang, LIANG Wen-Jie, WANG En-Ge 067302 A First-principles Study of Spin-polarized Transport Properties of a Co-coordination Complex WU Qiu-Hua, ZHAO Peng, LIU De-Sheng 067303 Single-ZnO-Nanobelt-Based Single-Electron Transistors JI Xiao-Fan, XU Zheng, CAO Shuo, QIU Kang-Sheng, TANG Jing, ZHANG Xi-Tian, XU Xiu-Lai

067304 Surface States of Bi2Se3 Nanowires in the Presence of Perpendicular Magnetic Fields SHI Li-Kun, LOU Wen-Kai 067305 Weak Electron-Phonon Coupling and Unusual Electron Scattering of Topological Surface States in Sb(111) by Laser-Based Angle-Resolved Photoemission Spectroscopy XIE Zhuo-Jin, HE Shao-Long, CHEN Chao-Yu, FENG Ya, YI He-Mian, LIANG Ai-Ji, ZHAO Lin, MOU Dai-Xiang, HE Jun-Feng, PENG Ying-Ying, LIU Xu, LIU Yan, LIU Guo-Dong, DONG Xiao-Li, YU Li, ZHANG Jun, ZHANG Shen-Jin, WANG Zhi-Min, ZHANG Feng-Feng, YANG Feng, PENG Qin-Jun, WANG Xiao-Yang, CHEN Chuang-Tian, XU Zu-Yan, ZHOU Xing-Jiang

067401 Electronic and Optic Properties of Cubic Spinel CdX2O4 (X=In, Ga, Al) through Modiﬁed Becke–Johnson Potential A. Manzar, G. Murtaza, R. Khenata, Masood Yousaf, S. Muhammad, Hayatullah 067402 Anomalous Temperature Dependence of the Quality Factor in a Superconducting Coplanar Waveguide Resonator ZHOU Pin-Jia, WANG Yi-Wen, WEI Lian-Fu 067403 Observation of Strong-Coupling Pairing with Weakened Fermi-Surface Nesting at Optimal Hole Doping in Ca0.33Na0.67Fe2As2 SHI Ying-Bo, HUANG Yao-Bo, WANG Xiao-Ping, SHI Xun, ROEKEGHEM A-Van, ZHANG Wei-Lu, XU Na, RICHARD Pierre, QIAN Tian, RIENKS Emile, THIRUPATHAIAH S, ZHAO Kan, JIN Chang-Qing, SHI Ming, DING Hong 067404 Consistency between Itinerant and Local-Moment Pictures for Superconductivity in Alkaline Iron Selenide Superconductors LI Hai-Chao, XIANG Yuan-Yuan, WANG Qiang-Hua 067501 Structure Dependence of Magnetic Properties for Annealed GaMnN Films Grown by MOCVD JIANG Xian-Zhe, YANG Xue-Lin, JI Cheng, XING Hai-Ying, YANG Zhi-Jian, WANG Cun-Da, YU Tong-Jun, ZHANG Guo-Yi 067701 Charge Loss Characteristics of Diﬀerent Al Contents in a HfAlO Trapping Layer Investigated by Variable Temperature Kelvin Probe Force Microscopy ZHANG Dong, HUO Zong-Liang, JIN Lei, HAN Yu-Long, CHU Yu-Qiong, CHEN Guo-Xing, LIU Ming, YANG Bao-He 067801 Low Frequency Ultra-Thin Compact Metamaterial Absorber Comprising Split-Ring Resonators LIN Bao-Qin, DA Xin-Yu, ZHAO Shang-Hong, MENG Wen, LI Fan, ZHENG Qiu-Rong, WANG Bu-Hong 067802 A Model on the Mn2+ Luminescence Band Redshift with Mn(II) Doping and Aggregation within CdS:Mn Microwires MUHAMMAD Arshad Kamran, ZHANG Yong-You, LIU Rui-Bin, SHI Li-Jie, ZOU Bing-Suo 067803 Near-Infrared Properties of Hybridized Plasmonic Rectangular Split Nanorings LIAO Zhong-Wei, HUANG Ying-Zhou, WANG Xiao-Yong, CHAU Irene Yeung-Yeung, WANG Shu-Xia, WEN Wei-Jia

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY 068401 Inﬂuence of Electric Field Distribution on High-Power Array Antenna Radiation Pattern with Rectangular Aperture YANG Yi-Ming, YUAN Cheng-Wei, QIAN Bao-Liang

068402 Developments of High-Efficiency Flexible Cu(In,Ga)Se2 Thin Film Solar Cells on a Polyimide Sheet by Sodium Incorporation ZHANG Li, LIU Fang-Fang, LI Feng-Yan, HE Qing, LI Chang-Jian, LI Bao-Zhang, ZHU Hong-Bing 068501 Properties of Heat Generation in a Double Quantum Dot ZHOU Li-Ling, LI Yong-Jun, HU Hua 068502 High-Voltage AlGaN/GaN-Based Lateral Schottky Barrier Diodes KANG He, WANG Quan, XIAO Hong-Ling, WANG Cui-Mei, JIANG Li-Juan, FENG Chun, CHEN Hong, YIN Hai-Bo, WANG Xiao-Liang, WANG Zhan-Guo, HOU Xun 068701 Ion Binding Energies Determining Functional Transport of ClC Proteins YU Tao, GUO Xu, ZOU Xian-Wu, SANG Jian-Ping 068801 A Simple Interconnection Layer for Tandem Organic Solar Cells with Improved Efficiency and Fill Factor ZHENG Ke-Ning, YANG Li-Ying, CAO Huan-Qi, QIN Wen-Jing, YIN Shou-Gen 068901 Effect of Mixing Assortativity on Extreme Events in Complex Networks LING Xiang