费米气体光晶格模型的渐近轨线

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1555-1562.

• 论文 • 上一篇

费米气体光晶格模型的渐近轨线

欧阳成^1,*(),汪维刚²,莫嘉琪³

¹ 湖州师范学院理学院浙江湖州 313000
² 合肥幼儿师范高等专科学校合肥 230011
³ 安徽师范大学数学与统计学院安徽芜湖 241003

收稿日期:2018-11-09 出版日期:2019-12-26 发布日期:2019-12-28
通讯作者: 欧阳成 E-mail:oyc@zjhu.edu.cn
基金资助:
国家自然科学基金(11771005);浙江省自然科学基金(LY13A010005);安徽省教育厅自然科学重点基金(KJ2018A0964);安徽省教育厅自然科学重点基金(KJ2019A1261)

The Asymptotic Path Curve for Fermi Gases Optical Lattices Model

Cheng Ouyang^1,*(),Weigang Wang²,Jiaqi Mo³

¹ Faculty of Science, Huzhou University, Zhejiang Huzhou 313000
² Department of Basic, Hefei Preschool Education College, Hefei 230011
³ School of Mathematics & Statistics, Anhui Normal University, Anhui Wuhu 241003

Received:2018-11-09 Online:2019-12-26 Published:2019-12-28
Contact: Cheng Ouyang E-mail:oyc@zjhu.edu.cn
Supported by:
the NSFC(11771005);the Natural Science Foundation of Zhejiang Province(LY13A010005);the Natural Science Foundation of the Education Department of Anhui Province(KJ2018A0964);the Natural Science Foundation of the Education Department of Anhui Province(KJ2019A1261)

摘要/Abstract

摘要：

研究了一类费米（Fermi）气体光晶格轨线模型.首先求得了费米气体光晶格在典型模型轨线的精确解.然后由一组广义泛函分析变分理论，构造一组迭代系统，得到了费米气体光晶格非线性扰动模型轨线的任意次渐近解.该文在方法上较方便地得到轨线的渐近表示式.所用的方法和基本理论，具有广泛的实际应用价值.

关键词: 扰动, 轨线, 渐近解

Abstract:

A class of model for the Fermi gases optical lattices is investigated. Firstly, the exact solution of the path curve to typical Fermi gases optical lattices model is constructed. Then, from the generalized functional analysis variation theory it constructed a set of iterative system. The arbitrary order asymptotic solution of nonlinear disturbed model of the path curve to Fermi gases optical lattices is obtained. In this paper, there got asymptotic repressions of the path curve expediently in the method and the proposed method and with the basic theory has wide application values.

Key words: Disturbed, Path curves, Asymptotic solution

中图分类号:

O175.14

欧阳成,汪维刚,莫嘉琪. 费米气体光晶格模型的渐近轨线[J]. 数学物理学报, 2019, 39(6): 1555-1562.

Cheng Ouyang,Weigang Wang,Jiaqi Mo. The Asymptotic Path Curve for Fermi Gases Optical Lattices Model[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1555-1562.

参考文献

1	Anderson M H , Ensher J R , Matthews , et al. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science, 1995, 269 (5221): 198- 201
2	Stoyanov L , Mateshkov G , Zhekova M , et al. Far-field bearn reshaping by manipulating the topological charges of hexagonal optical vortex lattices. J of Optics, 2018, 20 (9): 095601
3	Guo W , Wang K , Wu H , et al. Optical chirality of heical quanturm dots. Nanoscience and Nanochnology Letters, 2018, 10 (7): 988- 992
4	李艳. 从光晶格中释放的超冷玻色气体密度-密度关联函数研究. 物理学报, 2014, 63 (6): 066701
4	Li Y . Theory of density-density correlations between ultracold Bosons released from optical lattices. Acta Phys Sinica, 2014, 63 (6): 066701
5	Men F D , Liu H , Fan Z L , et al. Relativistic thermodynamic properties of a weakly interacting Fermi gas. Chin Phys B, 2009, 18 (7): 2649- 2653
6	Wen W , Shen S Q , Huang G X . Propagation of sound and supersonic bright solitons in superfluid Fermi gases in BCS-BEC crossover. Phys Rev B, 2010, 81 (1): 014528
7	Wang G F , Fu L B , Liu J . Periodic modulation effect on self-trapping of two weakly coupled Bose-Einstein condensates. Phys Rev A, 2006, 73 (1): 013619
8	Qi P T , Duan W S . Tunneling dynamics and phase transition of a Bose-Fermi mixture in a double well. Phys Rev A, 2011, 84 (3): 033627
9	Adhikari S K , Malomed B A , Salasnich L , et al. Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials. Phys Rev A, 2010, 81 (5): 053630
10	Chen Y S , Adhikari S K . Localization of a Bose-Fermi mixture in a bichromatic optical lattice. Phys Rev A, 2011, 84 (2): 023632
11	Qi R , Yu X L , Li Z B , et al. Non-abelian josephson effect between two F=2 spinor Bose-Einstein condensates in double optical traps. Phys Rev Lett, 2009, 102 (18): 185301
12	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. 物理学报, 2007, 56 (8): 4348- 4352
12	Zang X F , Li J P , Tan L . Nonlinear dynamical properties of susceptibility of a spinor Bose-Einstein condensate with dipole-dipole interaction in a double-well potential. Acta Phys Sin, 2007, 56 (8): 4348- 4352
13	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. 物理学报, 2006, 55 (11): 5623- 5628
13	Ma Y , Fu L B , Yang Z A , et al. Dynamical phase changes of the self-trapping of Bose-Einstein condensates and its characteristic of entanglement. Acta Phys Sin, 2006, 55 (11): 5623- 5628
14	王文元, 蒙红娟, 杨阳, 等. 费米超流气体的非线性Landau-Zener隧穿. 物理学报, 2012, 61 (8): 087302
14	Wang W Y , Meng H J , Yang Y , et al. Variable space scale factor spherical coordinates and time-space metric. Acta Phys Sin, 2012, 61 (8): 087302
15	黄芳, 李海彬. 双势阱中玻色-爱因斯坦凝聚的绝热隧穿. 物理学报, 2011, 60 (2): 020303
15	Huang F , Li H B . Adiabatic tunneling of Bose-Einstein condensatein double-well potential. Acta Phys Sin, 2011, 60 (2): 020303
16	Modugno G , Roati G , Riboli F , et al. Collapse of a degenerate Fermi gases. Science, 2002, 297 (5590): 2240- 2243
17	Volz T , Durr S , Ernst S , et al. Characterization of elastic scattering near a Feshbach resonance in Rb-87. Phys Rev A, 2003, 68 (1): 010702
18	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. 物理学报, 2013, 62 (13): 130308
18	Gou X Q , Yan M , Ling W D , et al. Self-trapping and periodic modulation of Fermi gases in optical lattices. Acta Phys Sin, 2013, 62 (13): 130308
19	He J H , Wu G C , Austin F . The variational iteration method which should be followed. Nonlinear Sci Lett A, 2010, 1 (1): 1- 30
20	He J H . Frontier of modern textile engineering and short remarks on some topics in physics. Inter J Nonlinear Scoences and Nimweical Simulation, 2010, 11 (7): 555- 563
21	He J H , Wu X H . Construction of solitary solution and compacton-like solution by variational iteration method. Chaos Solitions & Fractals, 2006, 29 (1): 108- 113
22	Mo J Q . Homotopiv mapping solving method for gain fluency of a laser pulse amplifier. Science in China Ser G, 2009, 39 (7): 1007- 1010
23	Mo J Q . Variational iteration solving method for a class of generalized Boussinesq equation. Chin Phys Lett, 2009, 26 (6): 060202
24	Mo J Q , Lin W T , Lin Y H . Asymptotic solution for the El Nino time delay sea-air oscillator model. Chin Phys B, 2011, 20 (7): 070205
25	Mo J Q , Lin Y H , Lin W T , Chen L H . Perturbed solving method for interdecadal sea-air oscillator model. Chin Geographical Sci, 2012, 22 (1): 42- 47
26	Mo J Q , Lin W T . Generalized variation iteration solution of an atmosphere-ocean oscillator model for global climateplexity. J Sys Sci Complexity, 2011, 24 (2): 271- 276
27	欧阳成, 姚静荪, 石兰芳, 等. 一类尘埃等离子体孤子解. 物理学报, 2014, 63 (11): 110203
27	Ouyang C , Yao J S , Shi L F , et al. Solitary wave solution for a class of dusty plasma. Acta Phys Sin, 2014, 63 (11): 110203
28	欧阳成, 陈贤峰, 莫嘉琪. 广义扰动Nizhnik-Novikov-Veselov系统的孤波解的孤波解. 系统科学与数学, 2017, 37 (3): 908- 917
28	Ouyang C , Chen X F , Mo J Q . The solutions to solitary wave for generalized disturbed Nizhnik-Novikov-Vedelov system. J Sys Sci Math, 2017, 37 (3): 908- 917
29	欧阳成, 姚静荪, 石兰芳, 等. 一类广义鸭轨迹系统轨线的构造. 物理学报, 2012, 61 (3): 030202
29	Ouyang C , Yao J S , Shi L F , et al. Constructing path curve for a class of generalized phase tracks of canard system. Acta Phys Sin, 2012, 61 (3): 030202
30	欧阳成, 林万涛, 程荣军, 等. 一类厄尔尼诺海-气时滞振子的渐近解. 物理学报, 2013, 62 (6): 060201
30	Ouyang C , Lin W T , Cheng R J , et al. A class of asymptotic solution of sea-air time delay oscillator for the Elnino-southern oscillation mechanism. Acta Phys Sin, 2013, 62 (6): 060201
31	Ouyang C , Cheng L H , Mo J Q . Solving a class of burning disturbed problem with shock layer. Chin Phy B, 2012, 21 (5): 050203
32	Wang W G , Shi L F , Han X L , et al. Singular perturbation problem for reaction diffusion tiime delay equation. Chin J Engineering Math, 2015, 32 (2): 291- 297
33	汪维刚, 林万涛, 石兰芳, 等. 非线性扰动时滞长波系统孤波解. 物理学报, 2014, 63 (11): 110204
33	Wang W G , Lin W T , Shi L F , et al. Approximate solution of solitary wave for nonlinear-disturbed time delay long-wave system. Acta Phys Sin, 2014, 63 (11): 110204
34	Wang W G , Shi L F , Xu Y H , et al. Generalized solution of the singularly perturbed boundary value problems for semilinear elliptic equation of higher order with two parameters. J Nankai Univ, 2014, 47 (2): 47- 81

[1]	武利猛, 李素红, 倪明康, 陆海波. 奇异摄动积分边值问题中的空间对照结构[J]. 数学物理学报, 2025, 45(5): 1565-1576.
[2]	曾夏萍, 卢文雯, 庞国萍, 梁志清. 具有季节性切换反应及脉冲扰动的鱼类单种群动力学模型[J]. 数学物理学报, 2025, 45(4): 1206-1216.
[3]	陈雪姣, 李丹丹, 石金诚, 曾鹏. 棱柱体中调和方程对基底扰动的连续依赖性[J]. 数学物理学报, 2025, 45(1): 101-109.
[4]	张胜良, 钱艳艳. 随机扰动下三阶MQ拟插值在导数逼近中的应用研究[J]. 数学物理学报, 2025, 45(1): 180-188.
[5]	韦华全, 吴辉, 刘晓冀, 靳宏伟. $\mathfrak{m}$-WG 逆的性质和计算[J]. 数学物理学报, 2024, 44(3): 547-562.
[6]	廖远康. 粘性依赖于密度的一维等熵可压缩 Navier-Stokes 方程组粘性激波的非线性稳定性[J]. 数学物理学报, 2023, 43(4): 1149-1169.
[7]	建芒芒, 郑素佩, 封建湖, 翟梦情. 浅水波方程熵稳定格式的保平衡性[J]. 数学物理学报, 2023, 43(2): 491-504.
[8]	聂嘉乐,余旌胡. 一类受随机扰动的动态优化问题的环境检测与响应[J]. 数学物理学报, 2022, 42(5): 1560-1574.
[9]	范楠,王才士,姬红. Bernoulli泛函上典则酉对合的扰动[J]. 数学物理学报, 2022, 42(4): 969-977.
[10]	张仲华,张倩. 转换机制下具有非线性扰动的随机SIVS传染病模型的定性分析[J]. 数学物理学报, 2021, 41(4): 1218-1234.
[11]	李海侠. 一类具有毒素的非均匀chemostat模型正解的存在性和唯一性[J]. 数学物理学报, 2020, 40(5): 1175-1185.
[12]	武利猛,倪明康,李素红,陆海波. 带有积分边界条件的奇异摄动边值问题的渐近解[J]. 数学物理学报, 2020, 40(5): 1192-1203.
[13]	梁文翠,张正杰. Kirchhoff型方程有关的非线性方程多解的存在性[J]. 数学物理学报, 2020, 40(4): 842-849.
[14]	张雅轩,许跟起,郭燕妮. 带有未知内部扰动的星形Euler-Bernoulli梁网络的指数跟踪控制[J]. 数学物理学报, 2019, 39(3): 596-610.
[15]	付盈洁,蓝桂杰,张树文,魏春金. 污染环境下具有脉冲输入的随机捕食-食饵模型的动力学研究[J]. 数学物理学报, 2019, 39(3): 674-688.

费米气体光晶格模型的渐近轨线

The Asymptotic Path Curve for Fermi Gases Optical Lattices Model

RichHTML

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0