Study on Path Curves of a Class of Fermi Gases in Optical Lattices With Nonlinear Mechanism

SHI Juan-rong; ZHU Min; MO Jia-qi

doi:10.21656/1000-0887.370046

Volume 38 Issue 4

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(4): 477-485

SHI Juan-rong, ZHU Min, MO Jia-qi. Study on Path Curves of a Class of Fermi Gases in Optical Lattices With Nonlinear Mechanism[J]. Applied Mathematics and Mechanics, 2017, 38(4): 477-485. doi: 10.21656/1000-0887.370046

Citation:

PDF( 538 KB)

Study on Path Curves of a Class of Fermi Gases in Optical Lattices With Nonlinear Mechanism

doi: 10.21656/1000-0887.370046

¹Anhui Technical College of Mechanical and Electrical Engineering, Wuhu, Anhui 241002, P.R.China;²Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Funds: The National Natural Science Foundation of China(41275062；11202106)

Received Date: 2016-02-13
Rev Recd Date: 2016-03-13
Publish Date: 2017-04-15

Abstract

Abstract

A nonlinear disturbed model for a class of Fermi gases in optical lattices was investigated. Firstly, in the nondisturbed case, the exact solution of the model path curves of Fermi gases in optical lattices was given. Secondly, the generalized functional analysis homotopic mapping was introduced and an iterative system was constructed, the arbitrary order asymptotic solution to the nonlinear disturbed model for the path curves of Fermi gases in optical lattices was obtained. Finally, a nonlinear small disturbance system was studied. With the proposed method, the asymptotic expressions of the path curves can be conveniently formulated and further extended.
- disturbed,
- path curve,
- functional

FullText(HTML)

References(36)

References

[1]	Anderson M H, Ensher J R, Matthews M R,et al. Observation of Bose-Einstein condensation in a dilute atomic vapor[J]. Science,1995,269(5221): 198-201.
[2]	MEN Fu-dian, LIU Hui, FAN Zhao-lan, et al. Relativistic thermodynamic properties of a weakly interacting Fermi gas[J]. Chinese Physics B, 2009,18 (7): 2649-2653.
[3]	马云, 傅立斌, 杨志安, 等. 玻色-爱因斯坦凝聚体自囚禁现象的动力学相变及其量子纠缠特性[J]. 物理学报, 2006,55(11): 5623-5628.(MA Yun, FU Li-bing, YANG Zhi-an, et al. Dynamical phase changes of the self-trapping of Bose-Einstein condensates and its characteristic of entanglement[J]. Acta Physica Sinica,2006,55(11): 5623-5628.(in Chinese))
[4]	WEN Wen, SHEN Shun-qing, HUANG Guo-xiang. Propagation of sound and supersonic bright solitons in superfluid Fermi gases in BCS-BEC crossover[J]. Physical Review B,2010,81(1): 014528.
[5]	臧小飞, 李菊萍, 谭磊. 偶极-偶极相互作用下双势阱中旋量玻色-爱因斯坦凝聚磁化率的非线性动力学性质[J]. 物理学报, 2007,56(8): 4348-4352.(ZANG Xiao-fei, LI Ju-ping, TAN Lei. Nonlinear dynamical properties of susceptibility of a spinor Bose-Einstein condensate with dipole-dipole interaction in a double-well potential[J]. Acta Physica Sinica,2007,56(8): 4348-4352.(in Chinese))
[6]	WANG Guan-fang, FU Li-bin, LIU Jie. Periodic modulation effect on self-trapping of two weakly coupled Bose-Einstein condensates[J]. Physical Review A,2006,73(1): 013619-1- 013619-7.
[7]	QI Peng-tang, DUAN Wen-shan. Tunneling dynamics and phase transition of a Bose-Fermi mixture in a double well[J]. Physical Review A,2011,84(3): 033627-1-033627-8.
[8]	Adhikari S K, Malomed B A, Salasnich L, et al. Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials[J]. Physical Review A,2010,〖STHZ〗 81(5): 053630-1-053630-9.
[9]	CHENG Yong-shan, Adhikari S K. Localization of a Bose-Fermi mixture in a bichromatic optical lattice[J].Physical Review A,2011,84(2): 023632-1-023632-7.
[10]	QI Ran, YU Xiao-lu, Li Z B, et al. Non-Abelian Josephson effect between two F=2 spinor Bose-Einstein condensates in double optical traps[J]. Physical Review Letters, 2009,102(18): 185301-1-185301-4.
[11]	王文元, 蒙红娟, 杨阳, 等. 空间变尺度因子球坐标系与四维时空度规[J]. 物理学报, 2012,61(8): 087302.(WANG Wen-yuan, MENG Hong-juan, YANG Yang, et al. Variable space scale factor spherical coordinates and time-space metric[J].Acta Physica Sinica, 2012,61(8): 087302.(in Chinese))
[12]	黄芳, 李海彬. 双势阱中玻色-爱因斯坦凝聚的绝热隧穿[J]. 物理学报, 2011,〖STHZ〗 60(2): 020303.(HUANG Fang, LI Hai-bing. Adiabatic tunneling of Bose-Einstein condensatein double-well potential[J].Acta Physica Sinica, 2011,60(2): 020303.(in Chinese))
[13]	Modugno G, Roati G, Riboli F, et al. Collapse of a degenerate Fermi gas[J]. Science,2002,297(5590): 2240-2243.
[14]	Volz T, Dürr S, Ernst S, et al. Characterization of elastic scattering near a Feshbach resonance in Rb-87[J].Physical Review A,2003,68(1): 010702.
[15]	苟学强，闫明，令伟栋，等. 费米气体在光晶格中的自俘获现象及其周期调制[J]. 物理学报,2013,62(13): 130308.(GOU Xue-qiang, YAN Ming, LING Wei-dong, et al. Self-trapping and periodic modulation of Fermi gases in optical lattices[J]. Acta Physica Sinica,2013,62(13): 130308.(in Chinese))
[16]	MO Jia-qi. Singular perturbation for a class of nonlinear reaction diffusion systems[J]. Science in China（Ser A）,1989,32(11): 1306-1315.
[17]	MO Jia-qi. Homotopiv mapping solving method for gain fluency of a laser pulse amplifier[J]. Science in China（Ser G）,2009,39(7): 1007-1010.
[18]	MO Jia-qi, LIN Shu-rong. The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation[J]. Chinese Physics B,2009,18(9): 3628-3631.
[19]	莫嘉琪, 陈贤峰. 一类广义非线性扰动色散方程孤立波的近似解[J]. 物理学报, 2010,50(3): 1403-1408.(MO Jia-qi, CHEN Xian-feng. Approximate solution of solitary wave for a class of generalized nonlinear disturbed dispersive equation[J]. Acta Physica Sinica,2010,50(3): 1403-1408.(in Chinese))
[20]	MO Jia-qi, CHEN Xian-feng. Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation[J]. Chinese Physics B, 2010,19(10): 100203.
[21]	MO Jia-qi. Solution of travelling wave for nonlinear disturbed long-wave system[J]. Communications in Theoretical Physics, 2011,55(3): 387-390.
[22]	MO Jia-qi, LIN Wan-tao, LIN Yi-hua. Asymptotic solution for the El Nio time delay sea-air oscillator model[J]. Chinese Physics B,2011,20(7): 070205.
[23]	莫嘉琪. 扰动Vakhnenko方程物理模型的行波解[J]. 物理学报, 2011,60(9): 090203.(MO Jia-qi. Travelling wave solution of disturbed Vakhnenko equation for physical model travelling wave solution of disturbed Vakhnenko equation for physical model[J]. Acta Physica Sinica,2011,60(9): 090203.(in Chinese))
[24]	莫嘉琪，程荣军，葛红霞. 具有控制项的弱非线性发展方程行波解[J]. 物理学报, 2011,60(5): 050204.(MO Jia-qi, CHENG Rong-jun, GE Hong-xia. Travelling wave solution of the weakly nonlinear evolution equation with control term[J]. Acta Physica Sinica,2011,60(5): 050204.(in Chinese))
[25]	莫嘉琪. 一类非线性尘埃等离子体孤波解[J]. 物理学报, 2011,60(3): 030203.(MO Jia-qi. The solution for a class of nonlinear solitary waves in dusty plasma[J]. Acta Physica Sinica, 2011,60(3): 030203.(in Chinese))
[26]	MO Jia-qi. Solution of travelling wave for nonlinear disturbed long-wave system[J]. Communications in Theoretical Physics,2011,55(2): 387-390.
[27]	史娟荣, 石兰芳, 莫嘉琪. 一类非线性强阻尼扰动展方程的解[J]. 应用数学和力学, 2014,35(9): 1046-1054.(SHI Juan-rong, SHI Lan-fang, MO Jia-qi. The solutions for a class of nonlinear disturbed evolution equations[J]. Applied Mathematics and Mechanics,2014,35(9): 1046-1054.(in Chinese))
[28]	史娟荣, 吴钦宽, 莫嘉琪. 非线性扰动广义NNV系统的孤子渐近行波解[J]. 应用数学和力学, 2015,36(9): 1003-1010.(SHI Juan-rong, WU Qin-kuan, MO Jia-qi. Asymptotic travelling wave solution of soliton for the nonlinear disturbed generalized NNV system[J]. Applied Mathematics and Mechanics,2015,36(9): 1003-1010.(in Chinese))
[29]	史娟荣, 朱敏, 莫嘉琪. 广义Schrdinger扰动耦合系统孤子解[J]. 应用数学和力学, 2016,37(3): 319-330.(SHI Juan-rong, ZHU Ming, MO Jia-qi. Solitary olutions to generalized Schrdinger disturbed coupled systems[J]. Applied Mathematics and Mechanics,2016,37(3): 319-330.(in Chinese))
[30]	SHI Juan-rong, LIN Wan-tao, MO Jia-qi. The singularly perturbed solution for a class of quasilinear nonlocal problem for higher two parameters[J]. J Nankai Univ,2015,48(1): 85-91.
[31]	石兰芳, 陈贤峰, 韩祥临, 等. 一类Fermi气体在非线性扰动机制中轨线的渐近表示[J]. 物理学报, 2014,63(6): 060204.(SHI Lan-fang, CHEN Xian-feng, HAN Xiang-lin, et al. Asymptotic expressions of path curve for a class of Fermi gases in nonlinear disturbed mechanism[J]. Acta Physica Sinica, 2014,63(6): 060204.(in Chinese))
[32]	Liao S J. Beyond Perturbation-Introduction to the Homotopy Analysis Method [M]. Boca Raton: Chapman & Hall/CRC, 2003.
[33]	Liao S J. Beyond Perturbation: Introduction to the Homotopy Analysis Method [M]. New York: CRC Press Co, 2004.
[34]	Liao S J. Homotopy Analysis Method in Nonlinear Differential Equations [M]. Heidelberg: Springer & Higher Education Press, 2012.
[35]	de Jager E M, JIANG Fu-ru. The Theory of Singular Perturbation [M]. Amsterdam: North-Holland Publishing Co, 1996.
[36]	Barbu L, Morosanu G. Singularly Perturbed Boundary-Value Problems [M]. Basel: Birkhauserm Verlag AG , 2007.