非相对论弱相互作用玻色气体的有效场理论处理

徐岩; 樊炜; 冀彦君; 宋仁刚; 陈兵; 赵振华; 陈达

doi:10.7498/aps.63.040501

摘要

采用有效场理论研究了非相对论弱相互作用玻色-爱因斯坦凝聚量子气体的一般性质. 在分析了系统的不可重整化性质后，从有效拉氏量出发，计算了最低阶环路修正下拉氏量参量的运动耦合常数（running coupling constant）的形式，并且得到了相应的微分方程. 研究结果表明，不同于相对论玻色气体的有效理论，对非相对论弱相互作用的玻色气体，可以移除该有效理论中的内禀能量尺度，即可令该有效理论的内禀能量尺度取无穷大值. 所得的分析结果将有助于对玻色-爱因斯坦凝聚的临界性质和行为的深入研究.

关键词:

Abstract

In this paper we study the theory of nonrelativistic weakly interacting Bose gas from the point of view of effective field theory. Firstly, the nonrenormalizability of the theory is briefly discussed. Then, starting from the effective Lagrangian, the lowest order contributions of Feynman diagrams are calculated for the parameters in the effective Lagrangian. These illustrate the running coupling constant phenomenon. After that, the differential align of the parameters in the effective Lagrangian is obtained. We show that the intrinsic energy scale of this effective theory can be removed, while it is not possible to do so for relativistic Bose gas. Our results can help to study the critical behavior of weakly interacting Bose gas.

Keywords:

作者及机构信息

1.
山东科技大学理学院应用物理系, 青岛 266590

基金项目: 国家自然科学基金（批准号：11105086）、山东省中青年科学家奖励基金（批准号：BS2011DX029, ZR2013AQ016）、青岛市科技计划（批准号：11-2-4-4-（6）-jch）和山东科技大学杰出青年基金（批准号：2011KYJQ101）资助的课题.

Authors and contacts

1.
College of Science, Shandong University of Science and Technology, Qingdao 266590, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11105086), the Natural Science Foundation of Shandong Province, China (Grant Nos. BS2011DX029, ZR2013AQ016), the Basic Scientific Research Project of Qingdao, China (Grant No. 11-2-4-4-(6)-jch), and the Shandong University of Science and Technology Research Fund for Distinguished Young Scholars, China (Grant No. 2011KYJQ101).

参考文献

[1]	Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[2]	Davis K B, Mewes M O, Andrews M R, van Druten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969
[3]	Burnett K, Edwards M, Clark C W 1999 Phys. Today 52 37
[4]	Leggett A J 2001 Rev. Mod. Phys. 73 307
[5]	Andersen J O 2004 Rev. Mod. Phys. 76 599
[6]	Boettcher I, Pawlowski J M, Diehl S 2012 Nucl. Phys. B 228 63
[7]	Fisher M P, Weichman P B, Grinstein G, Fisher D S 1989 Phys. Rev. B 40 546
[8]	Bloch I, Dalibard J, Zwerger W 2008 Rev. Mod. Phys. 80 885
[9]	Haugset T, Haugerud H, Ravndal F 1998 Annals Phys. 266 27
[10]	Braaten E, Nieto A 1999 Eur. Phys. J. B 11 143
[11]	Braaten E, Hammer H W, Mehen T 2002 Phys. Rev. Lett. 88 040401
[12]	Braaten E, Hammer H W, Hermans S 2001 Phys. Rev. A 63 063609
[13]	Altland A 2010 Condensed Matter Field Theory. (London: Cambridge University Press) p251
[14]	Tsvelik A 1996 Quantum Field Theory in Condensed Matter Physics (London: Cambridge University Press) p30
[15]	Schakel A 2008 Boulevard of Broken Symmetries: Effective Field Theories of Condensed Matter (Singapore: World Scientific Press) p95
[16]	Srednicki M 2007 Quantum Field Theory (London: Cambridge University Press) p129
[17]	Maggiore M 2005 A Modern Introduction to Quantum Field Theory (London: Oxford University Press) p135
[18]	Chen X W, Fang Z Y, Zhang J W, Zhong T, Tu W X 2011 Acta Phys. Sin. 60 021101 (in Chinese) [陈学文, 方祯云, 张家伟, 钟涛, 涂卫星 2011 物理学报 60 021101]
[19]	Polyanin A D, Manzhirov A V 2007 Handbook of Mathematics for Engineers and Scientists (Boca Raton FL: Chapman & Hall/CRC Press) p372
[20]	Wilson K G 1971 Phys. Rev. B 4 3184
[21]	Xu Y, Xiong Z Z, Li Z X, Chen B, Tan L 2009 Chin. Phys. B 18 4734
[22]	Fan W, Xu Y, Chen B, Chen Z Y, Feng X L, Oh C H 2012 Phys. Rev. A 85 013645

施引文献

[1]	Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
[2]	Davis K B, Mewes M O, Andrews M R, van Druten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969
[3]	Burnett K, Edwards M, Clark C W 1999 Phys. Today 52 37
[4]	Leggett A J 2001 Rev. Mod. Phys. 73 307
[5]	Andersen J O 2004 Rev. Mod. Phys. 76 599
[6]	Boettcher I, Pawlowski J M, Diehl S 2012 Nucl. Phys. B 228 63
[7]	Fisher M P, Weichman P B, Grinstein G, Fisher D S 1989 Phys. Rev. B 40 546
[8]	Bloch I, Dalibard J, Zwerger W 2008 Rev. Mod. Phys. 80 885
[9]	Haugset T, Haugerud H, Ravndal F 1998 Annals Phys. 266 27
[10]	Braaten E, Nieto A 1999 Eur. Phys. J. B 11 143
[11]	Braaten E, Hammer H W, Mehen T 2002 Phys. Rev. Lett. 88 040401
[12]	Braaten E, Hammer H W, Hermans S 2001 Phys. Rev. A 63 063609
[13]	Altland A 2010 Condensed Matter Field Theory. (London: Cambridge University Press) p251
[14]	Tsvelik A 1996 Quantum Field Theory in Condensed Matter Physics (London: Cambridge University Press) p30
[15]	Schakel A 2008 Boulevard of Broken Symmetries: Effective Field Theories of Condensed Matter (Singapore: World Scientific Press) p95
[16]	Srednicki M 2007 Quantum Field Theory (London: Cambridge University Press) p129
[17]	Maggiore M 2005 A Modern Introduction to Quantum Field Theory (London: Oxford University Press) p135
[18]	Chen X W, Fang Z Y, Zhang J W, Zhong T, Tu W X 2011 Acta Phys. Sin. 60 021101 (in Chinese) [陈学文, 方祯云, 张家伟, 钟涛, 涂卫星 2011 物理学报 60 021101]
[19]	Polyanin A D, Manzhirov A V 2007 Handbook of Mathematics for Engineers and Scientists (Boca Raton FL: Chapman & Hall/CRC Press) p372
[20]	Wilson K G 1971 Phys. Rev. B 4 3184
[21]	Xu Y, Xiong Z Z, Li Z X, Chen B, Tan L 2009 Chin. Phys. B 18 4734
[22]	Fan W, Xu Y, Chen B, Chen Z Y, Feng X L, Oh C H 2012 Phys. Rev. A 85 013645

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