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利用能量泛函变分法研究了一维Bose-Fermi系统稳定基态的存在条件.根据Bose-Fermi系统的Lagrange量可以得到三维Bose-Fermi体系所满足的非线性动力学方程组.当外势阱的横向囚禁频率远大于轴向囚禁频率时,体系可以当作一维模型来处理.从描述三维体系的动力学方程可以得到描述一维体系的动力学方程,选取适当的无量纲参数,可以对一维动力学方程组进行无量纲处理,得到数值计算和理论分析中常用到的无量纲方程.选择高斯型试探解(简单孤立子解),利用能量泛函变分法得到一维Bose-Fermi体系稳定的
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关键词:
- Bose-Fermi /
- 稳定性 /
- 基态 /
- 临界条件
In one-dimensional trapped Bose-Fermi mixture, described by time-dependent one-dimensional nonlinear equations that are derived from a three-dimensional Bose-Fermi system, we study the effect of atom-interactions on stability using a Gaussian Variational approach. We investigate the stable and the unstable conditions as functions of the atoms number and s-wave scattering length. We find that the interaction between the different species of atoms has significant effect on the stability of Bose-Fermi mixture. We also give critical conditions of the atoms number and s-wave scattering length for both special and general cases.-
Keywords:
- Bose-Fermi /
- stability /
- ground state /
- critical condition
[1] Adhikari S K 2005 Phys. Rev. A 72 053608
[2] [3] Adhikari S K, Salasnich L 2007 Phys. Rev. A 76 023612
[4] [5] Adhikari S K 2004 Phys. Rev. A 70 043617
[6] Adhikari S K 2006 Phys. Rev. A 73 043619
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[14] Ma Y, Fu L B, Yang Z A 2006 Acta phys. Sin. 55 5628 (in Chinese) [马 云、 傅立斌、 杨志安 2006 55 5628]
[15] [16] [17] Liu Z Z, Yang Z A 2007 Acta phys. Sin. 56 1245 (in Chinese) [刘泽专、 杨志安 2007 56 1245]
[18] [19] Zhao X D, Xie Z W, Zhang W P 2007 Acta phys. Sin. 56 6358 (in Chinese) [赵兴东、 谢征微、 张卫平 2007 56 6358]
[20] Zhou X Y, Mu A X, Xue J K 2007 Chin. Phys. 16 3197
[21] [22] [23] Zhang L P, Xue J K 2008 Chin. Phys. B 17 2594
[24] Huang C C, Wu W C 2007 Phys. Rev. A 75 023609
[25] [26] [27] Truscott A G, Strecker K E, McAlexander W I, Partridge G B, Hulet R G 2001 Science 291 2570
[28] Schreck F, Khaykovich L, Corwin K L, Ferrari G, Bourdel T, Cubizolles J, Salomon C 2001 Phys. Rev. Lett. 87 080403
[29] [30] Hadzibabic Z, Stan C A, Dieckmann K, Gupta S, Zwierlein M W, Grlitz A, Ketterle W 2002 Phys. Rev. Lett. 88 160401
[31] [32] [33] Goldwin J, Papp S B, DeMarco B, Jin D S 2002 Phys. Rev. A 65 021402
[34] Strecker K E, Partridge G B, Hulet R G 2003 Phys. Rev. Lett. 91 080406
[35] [36] Dong L W, Wang J D, Wang H, Yin G Y 2009 Phys. Rev. A 79 013807
[37] [38] Baizakov B B, Malomed B A, Salerno M 2006 Phys. Rev. E 74 066615
[39] [40] Li H and Wang D N 2009 Chin. Phys. B 18 4726
[41] [42] [43] Li H and Wang D N 2009 Chin. Phys. B 18 2659
[44] [45] Xue J K, Zhang A X, Liu J 2008 Phys. Rev. A 77 013602
[46] Wang J J, Zhang A X, Zhang K Z,Ma J, Xue J K 2010 Phys. Rev. A 81 033607
[47] -
[1] Adhikari S K 2005 Phys. Rev. A 72 053608
[2] [3] Adhikari S K, Salasnich L 2007 Phys. Rev. A 76 023612
[4] [5] Adhikari S K 2004 Phys. Rev. A 70 043617
[6] Adhikari S K 2006 Phys. Rev. A 73 043619
[7] [8] Modugno M, Ferlaino F, Riboli F, Roati G, Modugno G, Inguscio M 2003 Phys. Rev. A 68 043626
[9] [10] Morise H, Tsrumi T, Wadati M 2000 Physica A 281 432
[11] [12] [13] Wang G F, Fu L B, Zhao H, Liu J 2005 Acta phys. Sin. 54 5003 (in Chinese) [王冠芳、 傅立斌、 赵 鸿、 刘 杰 2005 54 5003]
[14] Ma Y, Fu L B, Yang Z A 2006 Acta phys. Sin. 55 5628 (in Chinese) [马 云、 傅立斌、 杨志安 2006 55 5628]
[15] [16] [17] Liu Z Z, Yang Z A 2007 Acta phys. Sin. 56 1245 (in Chinese) [刘泽专、 杨志安 2007 56 1245]
[18] [19] Zhao X D, Xie Z W, Zhang W P 2007 Acta phys. Sin. 56 6358 (in Chinese) [赵兴东、 谢征微、 张卫平 2007 56 6358]
[20] Zhou X Y, Mu A X, Xue J K 2007 Chin. Phys. 16 3197
[21] [22] [23] Zhang L P, Xue J K 2008 Chin. Phys. B 17 2594
[24] Huang C C, Wu W C 2007 Phys. Rev. A 75 023609
[25] [26] [27] Truscott A G, Strecker K E, McAlexander W I, Partridge G B, Hulet R G 2001 Science 291 2570
[28] Schreck F, Khaykovich L, Corwin K L, Ferrari G, Bourdel T, Cubizolles J, Salomon C 2001 Phys. Rev. Lett. 87 080403
[29] [30] Hadzibabic Z, Stan C A, Dieckmann K, Gupta S, Zwierlein M W, Grlitz A, Ketterle W 2002 Phys. Rev. Lett. 88 160401
[31] [32] [33] Goldwin J, Papp S B, DeMarco B, Jin D S 2002 Phys. Rev. A 65 021402
[34] Strecker K E, Partridge G B, Hulet R G 2003 Phys. Rev. Lett. 91 080406
[35] [36] Dong L W, Wang J D, Wang H, Yin G Y 2009 Phys. Rev. A 79 013807
[37] [38] Baizakov B B, Malomed B A, Salerno M 2006 Phys. Rev. E 74 066615
[39] [40] Li H and Wang D N 2009 Chin. Phys. B 18 4726
[41] [42] [43] Li H and Wang D N 2009 Chin. Phys. B 18 2659
[44] [45] Xue J K, Zhang A X, Liu J 2008 Phys. Rev. A 77 013602
[46] Wang J J, Zhang A X, Zhang K Z,Ma J, Xue J K 2010 Phys. Rev. A 81 033607
[47]
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