Ground-State Transition in a Two-Dimensional Frenkel–Kontorova Model
YUAN Xiao-Ping1,2, ZHENG Zhi-Gang1**
1Department of Physics and the Beijing-Hongkong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875 2Information Engineering School, Hangzhou Dianzi University, Hangzhou 310018
Ground-State Transition in a Two-Dimensional Frenkel–Kontorova Model
YUAN Xiao-Ping1,2, ZHENG Zhi-Gang1**
1Department of Physics and the Beijing-Hongkong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875 2Information Engineering School, Hangzhou Dianzi University, Hangzhou 310018
摘要The ground state of a generalized Frenkel–Kontorova model with a transversal degree of freedom is studied. When the coupling strength, K, and the frequency of a single−atom vibration in the transversal direction, ω0y, are increased, the ground state of the model undergoes a transition from a two−dimensional configuration to a one-dimensional one. This transition can manifest in different ways. Furthermore, we find that the prerequisite of a two-dimensional ground state is θ≠1/q.
Abstract：The ground state of a generalized Frenkel–Kontorova model with a transversal degree of freedom is studied. When the coupling strength, K, and the frequency of a single−atom vibration in the transversal direction, ω0y, are increased, the ground state of the model undergoes a transition from a two−dimensional configuration to a one-dimensional one. This transition can manifest in different ways. Furthermore, we find that the prerequisite of a two-dimensional ground state is θ≠1/q.
[1] Hamilton J C 2002 Phys. Rev. Lett. 88 126101
[2] Müller B, Fischer B, Nedelmann L, Fricke A and Kern K 1996 Phys. Rev. Lett. 76 2358
[3] Dubos P, Courtois H, Buisson O and Pannetier B 2001 Phys. Rev. Lett. 87 206801
[4] Kitamura M, Irie A and Oya G I 2007 Phys. Rev. B 76 064518
[5] Kautz R L, 1981 Appl. Phys. 52 3528
[6] Weiss M and Elmer F J 1996 Phys. Rev. B 53 7539
[7] Persson B N J 1998 Sliding Friction: Physical Principles and Applications (Berlin: Springer-Verlag)
[8] Lin M M, Duan W S and Chen J M 2010 Chin. Phys. B 19 026201
[9] Grüner G 1988 Rev. Mod. Phys. 60 1129
[10] McCarten J, DiCarlo D A, Maher M P, Adelman T L and Thorne R E 1992 Phys. Rev. B 46 4456
[11] Shao Z G, Yang L, Chan H K and Hu B 2009 Phys. Rev. E 79 061119
Shao Z G, Yang L, Zhong W R, He D H and Hu B 2008 Phys. Rev. E 78 061130
Hu B and Yang L 2005 Chaos 15 015119
[12] Wang B H, Kwong Y R, Hui P M and Hu B 1999 Phys. Rev. E 60 149
[13] Braun O M, Dauxois T, Paliy M V and Peyrard M 1997 Phys. Rev. Lett. 78 1295
Braun O M, Dauxois T, Paliy M V and Peyrard M 1997 Phys. Rev. E 55 3598
[14] Paliy M V, Braun O M, Dauxois T and Hu B 1997 Phys. Rev. E 56 4025
[15] Tekié J, He D H and Hu B 2009 Phys. Rev. E 79 036604
[16] Floría L M and Falo F 1992 Phys. Rev. Lett. 68 2713
[17] Zheng Z G, Hu B and Hu G 1998 Phys. Rev. B 58 5453
[18] Qin W X, Hu B and Zheng Z G 2005 Physica D 208 172
[19] Yuan X P, Chen H B and Zheng Z G 2006 Chin. Phys. 15 1464
Yuan X P and Zheng Z G 2007 Chin. Phys. Lett. 24 2513
[20] Braun O M, Paliy M V, Röder J and Bishop A R 2001 Phys. Rev. E 63 036129
[21] Savin A V, Zubova E A and Manevitch L I 2005 Phys. Rev. B 71 224303
[22] Li R T, Duan W S, Yang Y, Wang C L and Chen J M 2011 Europhys. Lett. 94 56003
[23] Braun O M, Chubykalo O A, Kivshar Yu S and Valkering T P 1998 Physica D 113 152
[24] Braun O M and Peyrard M 1995 Phys. Rev. E 51 4999
[25] Braun O M and Kivshar Yu S 1991 Phys. Rev. B 44 7694
[26] Braun O M 1990 Surf. Sci. 230 262
[27] Peyrard M and Aubry S 1983 J. Phys. C 16 1593
2011, Vol. 28 
