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有限温度下一维Gaudin-Yang模型的热力学性质

张天宝 俞玄平 陈阿海

有限温度下一维Gaudin-Yang模型的热力学性质

张天宝, 俞玄平, 陈阿海
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  • 本文通过数值求解有限温度下一维均匀费米Gaudin-Yang模型的热力学Bethe-ansatz方程, 研究了此模型的基本性质,得到了在给定的温度或给定的相互作用下, 化学势、相互作用、粒子密度和熵的相互变化图像. 对结果分析发现, 在给定温度和相互作用下, 熵随着化学势的变化有一个量子临界区域.
    • 基金项目: 国家自然科学基金(批准号: 11174253, 11374266)和浙江省自然科学基金(批准号: R6110175)资助的课题.
    [1]

    Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198

    [2]

    Feshbach H 1958 Ann. Phys. 5 357

    [3]

    Tiesinga E, Verhaar B J, Stoof H T C 1993 Phys. Rev. A 47 4114

    [4]

    DeMarco B, Jin D S 1999 Science 285 1703

    [5]

    Köhl M, Moritz H, Stöferle T, Gnter K, Esslinger T 2005 Phys. Rev. Lett. 94 080403

    [6]

    Geng T, Yan S B, Wang Y H, Yang H J, Zhang T C, Wang J M 2005 Acta Phys. Sin. 54 5104 (in Chinese) [耿涛, 闫树斌, 王彦华, 杨海菁, 张天才, 王军民 2005 物理学报 54 5104]

    [7]

    Cazalilla M A, Citro R, Giamarchi T, Orignac E, Rigol M 2011 Rev. Mod. Phys. 83 1405

    [8]

    Guan X W, Batchelor M T, Lee C H 2013 Rev. Mod. Phys. 85 1633

    [9]

    Gao X L 2010 Phys. Rev. B 81 104306

    [10]

    Li W, Gao X L, Kollath C, Polini M 2008 Phys. Rev. B 78 195109

    [11]

    Xu Z J, Liu X Y 2011 Acta Phys. Sin. 60 120305 (in Chinese) [徐志君, 刘夏吟 2011 物理学报 60 120305]

    [12]

    Astrakharchik G E, Blume D, Giorgini S, Pitaevskii L P 2004 Phys. Rev. Lett. 93 050402

    [13]

    van Amerongen A H, van Es J J P, Wicke P, Kheruntsyan K V, van Druten N J 2008 Phys. Rev. Lett. 100 090402

    [14]

    Moritz H, Stöferle T, Köhl M, Esslinger T 2003 Phys. Rev. Lett. 91 250402

    [15]

    Yang C N 1967 Phys. Rev. Lett. 19 1312

    [16]

    Gaudin M 1967 Phys. Lett. A 24 55

    [17]

    Menotti C, Stringari S 2002 Phys. Rev. A 66 043610

    [18]

    Gao X L, Asgari R 2008 Phys. Rev. A 77 033604

    [19]

    Gao X L, Polini M, Asgari R, Tosi M P 2006 Phys. Rev. A 73 033609

    [20]

    Guan L M, Chen S, Wang Y P, Ma Z Q 2009 Phys. Rev. Lett. 102 160402

    [21]

    Takahashi M 1971 Prog. Theor. Phys. 46 1388

    [22]

    Hu H, Gao X L, Liu X J 2014 Phys. Rev. A 90 013622

    [23]

    Lee J Y, Guan X W, Sakai K, Batchelor M T 2012 Phys. Rev. B 85 085414

    [24]

    Chen Y Y, Jiang Y Z, Guan X W, Zhou Q 2014 Nat. Commun. 5

    [25]

    Hoffman M D, Javernick P, Loheac A C, Porter W J, Anderson E R, Drut J E 2014 arXiv:1410.7370vl

    [26]

    Zhao E, Guan X W, Liu W V, Batchelor M T, Oshikawa M 2009 Phys. Rev. Lett. 103 140404

    [27]

    Batchelor M T, Foerster A, Guan X W, Kuhn C C N 2010 J. Stat. Mech. P12014

    [28]

    Klmper A, Pâţu O I 2011 Phys. Rev. A 84 051604

    [29]

    Kheruntsyan K V, Gangardt D M, Drummond P D, Shlyapnikov G V 2003 Phys. Rev. Lett. 91 040403

    [30]

    Kheruntsyan K V, Gangardt D M, Drummond P D, Shlyapnikov G V 2005 Phys. Rev. A 71 053615

    [31]

    Takahashi M 1972 Prog. Theor. Phys. 47 69

    [32]

    Usuki T, Kawakami N, Okiji A 1989 Phys. Lett. A 135 476

    [33]

    Usuki T, Kawakami N, Okiji A 1990 J.Phys. Soc. Jpn. 59 1357

    [34]

    Suzuki M 1985 Phys. Rev. B 31 2957

    [35]

    Suzuki M, Inoue M 1987 Prog. Theor. Phys. 78 787

    [36]

    Jttner G, Klmper A, Suzuki J 1998 Nucl. Phys. B 522 471

    [37]

    Klmper A, Bariev R Z 1996 Nucl. Phys. B 458 623

    [38]

    Takahashi M, Shiroishi M 2002 Phys. Rev. B 65 165104

    [39]

    Khatami E, Rigol M 2011 Phys. Rev. A 84 053611

    [40]

    Wolak M J, Rousseau V G, Miniatura C, Grémaud B, Scalettar R T, Batrouni G G 2010 Phys. Rev. A 82 013614

    [41]

    Snyder A, Tanabe I, De Silva T 2011 Phys. Rev. A 83 063632

    [42]

    Carmelo J M P, Gu S J, Sampaio M J 2014 J. Phys. 47 255004

    [43]

    Carmelo J M P, Gu S J, Sacramento P D 2013 Ann. Phys. 339 484

    [44]

    Chen F, Ying H P, Xu T F, Li W Z 1994 Acta Phys. Sin. 43 1672 (in Chinese) [陈锋, 应和平, 徐铁锋, 李文铸 1994 物理学报 43 1672]

    [45]

    Gao X L, Chen A H, Tokatly I V, Kurth S 2012 Phys. Rev. B 86 235139

    [46]

    Campo V L 2014 arXiv:1407.6726vl

    [47]

    Olshanii M 1998 Phys. Rev. Lett. 81 938

    [48]

    Dunjko V, Lorent V, Olshanii M 2001 Phys. Rev. Lett. 86 5413

    [49]

    Hu J H, Wang J J, Gao X L, Okumura M, Igarashi R, Yamada S, Machida M 2010 Phys. Rev. B 82 014202

    [50]

    Wei F X,Gao X L 2014 Journal of Zhejiang Normal University (Nat. Sci.) 37 54 (in Chinese) [卫福霞, 高先龙 2014 浙江师范大学学报(自然科学版) 37 54]

  • [1]

    Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198

    [2]

    Feshbach H 1958 Ann. Phys. 5 357

    [3]

    Tiesinga E, Verhaar B J, Stoof H T C 1993 Phys. Rev. A 47 4114

    [4]

    DeMarco B, Jin D S 1999 Science 285 1703

    [5]

    Köhl M, Moritz H, Stöferle T, Gnter K, Esslinger T 2005 Phys. Rev. Lett. 94 080403

    [6]

    Geng T, Yan S B, Wang Y H, Yang H J, Zhang T C, Wang J M 2005 Acta Phys. Sin. 54 5104 (in Chinese) [耿涛, 闫树斌, 王彦华, 杨海菁, 张天才, 王军民 2005 物理学报 54 5104]

    [7]

    Cazalilla M A, Citro R, Giamarchi T, Orignac E, Rigol M 2011 Rev. Mod. Phys. 83 1405

    [8]

    Guan X W, Batchelor M T, Lee C H 2013 Rev. Mod. Phys. 85 1633

    [9]

    Gao X L 2010 Phys. Rev. B 81 104306

    [10]

    Li W, Gao X L, Kollath C, Polini M 2008 Phys. Rev. B 78 195109

    [11]

    Xu Z J, Liu X Y 2011 Acta Phys. Sin. 60 120305 (in Chinese) [徐志君, 刘夏吟 2011 物理学报 60 120305]

    [12]

    Astrakharchik G E, Blume D, Giorgini S, Pitaevskii L P 2004 Phys. Rev. Lett. 93 050402

    [13]

    van Amerongen A H, van Es J J P, Wicke P, Kheruntsyan K V, van Druten N J 2008 Phys. Rev. Lett. 100 090402

    [14]

    Moritz H, Stöferle T, Köhl M, Esslinger T 2003 Phys. Rev. Lett. 91 250402

    [15]

    Yang C N 1967 Phys. Rev. Lett. 19 1312

    [16]

    Gaudin M 1967 Phys. Lett. A 24 55

    [17]

    Menotti C, Stringari S 2002 Phys. Rev. A 66 043610

    [18]

    Gao X L, Asgari R 2008 Phys. Rev. A 77 033604

    [19]

    Gao X L, Polini M, Asgari R, Tosi M P 2006 Phys. Rev. A 73 033609

    [20]

    Guan L M, Chen S, Wang Y P, Ma Z Q 2009 Phys. Rev. Lett. 102 160402

    [21]

    Takahashi M 1971 Prog. Theor. Phys. 46 1388

    [22]

    Hu H, Gao X L, Liu X J 2014 Phys. Rev. A 90 013622

    [23]

    Lee J Y, Guan X W, Sakai K, Batchelor M T 2012 Phys. Rev. B 85 085414

    [24]

    Chen Y Y, Jiang Y Z, Guan X W, Zhou Q 2014 Nat. Commun. 5

    [25]

    Hoffman M D, Javernick P, Loheac A C, Porter W J, Anderson E R, Drut J E 2014 arXiv:1410.7370vl

    [26]

    Zhao E, Guan X W, Liu W V, Batchelor M T, Oshikawa M 2009 Phys. Rev. Lett. 103 140404

    [27]

    Batchelor M T, Foerster A, Guan X W, Kuhn C C N 2010 J. Stat. Mech. P12014

    [28]

    Klmper A, Pâţu O I 2011 Phys. Rev. A 84 051604

    [29]

    Kheruntsyan K V, Gangardt D M, Drummond P D, Shlyapnikov G V 2003 Phys. Rev. Lett. 91 040403

    [30]

    Kheruntsyan K V, Gangardt D M, Drummond P D, Shlyapnikov G V 2005 Phys. Rev. A 71 053615

    [31]

    Takahashi M 1972 Prog. Theor. Phys. 47 69

    [32]

    Usuki T, Kawakami N, Okiji A 1989 Phys. Lett. A 135 476

    [33]

    Usuki T, Kawakami N, Okiji A 1990 J.Phys. Soc. Jpn. 59 1357

    [34]

    Suzuki M 1985 Phys. Rev. B 31 2957

    [35]

    Suzuki M, Inoue M 1987 Prog. Theor. Phys. 78 787

    [36]

    Jttner G, Klmper A, Suzuki J 1998 Nucl. Phys. B 522 471

    [37]

    Klmper A, Bariev R Z 1996 Nucl. Phys. B 458 623

    [38]

    Takahashi M, Shiroishi M 2002 Phys. Rev. B 65 165104

    [39]

    Khatami E, Rigol M 2011 Phys. Rev. A 84 053611

    [40]

    Wolak M J, Rousseau V G, Miniatura C, Grémaud B, Scalettar R T, Batrouni G G 2010 Phys. Rev. A 82 013614

    [41]

    Snyder A, Tanabe I, De Silva T 2011 Phys. Rev. A 83 063632

    [42]

    Carmelo J M P, Gu S J, Sampaio M J 2014 J. Phys. 47 255004

    [43]

    Carmelo J M P, Gu S J, Sacramento P D 2013 Ann. Phys. 339 484

    [44]

    Chen F, Ying H P, Xu T F, Li W Z 1994 Acta Phys. Sin. 43 1672 (in Chinese) [陈锋, 应和平, 徐铁锋, 李文铸 1994 物理学报 43 1672]

    [45]

    Gao X L, Chen A H, Tokatly I V, Kurth S 2012 Phys. Rev. B 86 235139

    [46]

    Campo V L 2014 arXiv:1407.6726vl

    [47]

    Olshanii M 1998 Phys. Rev. Lett. 81 938

    [48]

    Dunjko V, Lorent V, Olshanii M 2001 Phys. Rev. Lett. 86 5413

    [49]

    Hu J H, Wang J J, Gao X L, Okumura M, Igarashi R, Yamada S, Machida M 2010 Phys. Rev. B 82 014202

    [50]

    Wei F X,Gao X L 2014 Journal of Zhejiang Normal University (Nat. Sci.) 37 54 (in Chinese) [卫福霞, 高先龙 2014 浙江师范大学学报(自然科学版) 37 54]

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出版历程
  • 收稿日期:  2015-01-04
  • 修回日期:  2015-03-18
  • 刊出日期:  2015-08-05

有限温度下一维Gaudin-Yang模型的热力学性质

  • 1. 浙江师范大学物理系, 金华 321004;
  • 2. 伦敦大学学院物理与天文学系, 伦敦 WC1E 6BT
    基金项目: 

    国家自然科学基金(批准号: 11174253, 11374266)和浙江省自然科学基金(批准号: R6110175)资助的课题.

摘要: 本文通过数值求解有限温度下一维均匀费米Gaudin-Yang模型的热力学Bethe-ansatz方程, 研究了此模型的基本性质,得到了在给定的温度或给定的相互作用下, 化学势、相互作用、粒子密度和熵的相互变化图像. 对结果分析发现, 在给定温度和相互作用下, 熵随着化学势的变化有一个量子临界区域.

English Abstract

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