Discrete breathers in a model with Morse potentials

doi:10.1088/1674-1056/19/2/026302

中国物理B ›› 2010, Vol. 19 ›› Issue (2): 26302-026302.doi: 10.1088/1674-1056/19/2/026302

Discrete breathers in a model with Morse potentials

吕彬彬, 邓艳平, 田强

Department of Physics, Beijing Normal University, Beijing 100875, China

收稿日期:2009-04-09 修回日期:2009-06-02 出版日期:2010-02-15 发布日期:2010-02-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 1057411), and the Foundation for Researching Group by Beijing Normal University.

Discrete breathers in a model with Morse potentials

Lü Bin-Bin(吕彬彬)^†, Deng Yan-Ping(邓艳平), and Tian Qiang(田强)

Department of Physics, Beijing Normal University, Beijing 100875, China

Received:2009-04-09 Revised:2009-06-02 Online:2010-02-15 Published:2010-02-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 1057411), and the Foundation for Researching Group by Beijing Normal University.

摘要/Abstract

摘要： Under harmonic approximation, this paper discusses the linear dispersion relation of the one-dimensional chain. The existence and evolution of discrete breathers in a general one-dimensional chain are analysed for two particular examples of soft (Morse) and hard (quartic) on-site potentials. The existence of discrete breathers in one-dimensional and two-dimensional Morse lattices is proved by using rotating wave approximation, local anharmonic approximation and a numerical method. The localization and amplitude of discrete breathers in the two-dimensional Morse lattice with on-site harmonic potentials correlate closely to the Morse parameter a and the on-site parameter к.

Abstract: Under harmonic approximation, this paper discusses the linear dispersion relation of the one-dimensional chain. The existence and evolution of discrete breathers in a general one-dimensional chain are analysed for two particular examples of soft (Morse) and hard (quartic) on-site potentials. The existence of discrete breathers in one-dimensional and two-dimensional Morse lattices is proved by using rotating wave approximation, local anharmonic approximation and a numerical method. The localization and amplitude of discrete breathers in the two-dimensional Morse lattice with on-site harmonic potentials correlate closely to the Morse parameter a and the on-site parameter $\kappa$.

Key words: discrete breathers, Morse lattice, square lattice, on-site potential

中图分类号: (Localized modes)

63.20.Pw

63.20.D- (Phonon states and bands, normal modes, and phonon dispersion) 63.20.Ry (Anharmonic lattice modes)

吕彬彬, 邓艳平, 田强. Discrete breathers in a model with Morse potentials[J]. 中国物理B, 2010, 19(2): 26302-026302.

Lü Bin-Bin(吕彬彬), Deng Yan-Ping(邓艳平), and Tian Qiang(田强). Discrete breathers in a model with Morse potentials[J]. Chin. Phys. B, 2010, 19(2): 26302-026302.

参考文献 20

[1]	Sievers A J and Takeno S 1988 Phys. Rev. Lett. 61 970
[2]	Page J B 1991 Phys. Rev. B 41 7835
[3]	Mackay R S and Aubry S 1994 Nonlinearity 7 1623
[4]	Aubry S 1997 PhysicaD} 10 3 201
[5]	Flach S and Willis C R 1998 Phys. Rep. 295 181
[6]	Zhou Q, Lü B B and Tian Q 2009 Acta Phys. Sin. 58 411 (in Chinese)
[7]	Eisenberg H S, Silberberg Y, Morandotti R, Boyd A R and Aitchison JS 1998 Phys. Rev. Lett. 81 3383
[8]	Fleischer J W, Segev M, Efredmidis N K and Christodoulides D N 2003 Nature 4 22 147
[9]	Trias E, Mazo J J and Orlando T P 2000 Phys. Rev. Lett. 84 741
[10]	Binder P, Abraimov D, Ustinov A V, Flach S and Zolotaryuk Y 2000 Phys. Rev. Lett. 84 745
[11]	Sato M, Hubbard B E, Sievers A J, Ilic B, Czaplewski D Aand Craighead H G 2003 Phys. Rev. Lett. 90 044102
[12]	Sato M, Hubbard B E, Sievers A J, Ilic B and Craighead H G 2004 Europhys. Lett. 66 318
[13]	Lü B B, Zhou Q and Tian Q 2008 Journal ofBeijing Normal University(Natural Science) 44 476 (inChinese)
[14]	Lü B B and Tian Q 2008 Journal of BeijingNormal University(Natural Science) 44 581 (in Chinese)
[15]	Lü B B and Tian Q 2009 Chin. Phys. B 18 4393
[16]	Burlakov V M, Kiselev S A and Pyrkov V N 1990 Phys. Rev. B 42 4921
[17]	Flach S, Kladko K and Takeno S 1997 Phys. Rev. Lett. 79 4838
[18]	Tamga J M, Remoissenet M and Pouget J 1995 Phys. Rev. Lett. 75357
[19]	Sandusky K W and Page J B 1994 Phys. Rev. B 50 866
[20]	Dauxois T and Peyrard M 1993 Phys. Rev. Lett. 70 3935

Discrete breathers in a model with Morse potentials

Discrete breathers in a model with Morse potentials

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