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Based on the Heisenberg model, the anti-ferromagnet following the interaction suddenly switched-on at t=0 is considered in this paper. In the limit of low temperature, the time evolution of observables is analytically studied by utilizing the flow equation method. According to the unique feature of the system, the way to obtain the evolution of observables is shown and applied to the system we focused on. Further, special emphasis is laid on the application of the flow equation method to non-equilibrium magnetic systems so that the validity of the method applied to this kind of systems is traced. By means of this method, the evolution of magnetization of the ground state is traced in detail. It is found that the magnetization oscillates with time rather than converges,which is different from that of non-equilibrium Luttinger liquids.
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Keywords:
- non-equilibrium system /
- anti-ferromagnetic Heisenberg model /
- flow equation method /
- magnetization
[1] Stamper-Kurn D M, Miesner H J, Chikkatur A P, lnouye S, Stenger J, Ketterle W 1999 Phys. Rev. Lett. 83 661
[2] Wu H Y, Yin L 2006 Acta Phys. Sin. 55 490 (in Chinese) [武宏宇、 尹 澜 2006 55 490]
[3] He Z M, Wang D L, Zhang W X, Wang F J 2008 Chin. Phys. B 17 3640
[4] Chin C, Vuleti’c V, Kerman A J, Chu S 2001 Phys. Rev. Lett. 85 2717
[5] Loftus T, Regal C A, Ticknor C, Bohn J L, Jin D S 2002 Phys. Rev. Lett. 88 173201
[6] Greiner M, Mandel O, Esslinger T, Hnsch T W, Bloch I 2002 Nature 415 39
[7] Barouch E, McCoy B 1970 Phys. Rev. A 2 1075
[8] Stoferle T, Moritz H, Schori C, Kohl M, Esslinger T 2004 Phys. Rev. Lett. 92 130403
[9] Fertig C D, O’Hara K M, Huckans J H, Rolston S L, Phillips W D, Porto J V 2005 Phys. Rev. Lett. 94 120403
[10] Kinoshita T, Wenger T, Weiss D S 2006 Nature 440 900
[11] Zhao J M, Zhang L J, Li C Y, Jia S T 2008 Acta Phys. Sin. 57 2895 (in Chinese) [赵建明、 张临杰、 李昌勇、 贾锁堂 2008 57 2895]
[12] Schreck F Khaykovivh L, Corwin K L, Ferrari G, Bourdel T, Cubizolles J, Salomon C 2001 Phys. Rev. Lett. 87 080403
[13] Strecker K E, Partridge G B, Truscott A G, Hulet R G 2002 Nature 417 150
[14] Jiang Y R, Feng M, Gao K L, Zhu X W 2001 Chin. Phys. 10 202
[15] Calabrese P, Cardy J 2007 J. Stat. Mech. p06008
[16] Wegner F 1994 Ann. Phys. 3 77
[17] Glazek S D, Wilson K G 1994 Phys. Rev. D 49 4214
[18] Kehrein S 2006 The Flow Equation Approach to Many-Particle Systems (Berlin: Springer) p98
[19] Wang F, Zhang F S, Eric S 2003 Chin. Phys. 12 164
[20] Cazalilla M A 2006 Phys. Rev. Lett. 97 156403
[21] Moeckel M, Kehrein S 2008 Phys. Rev. Lett. 100 175702
[22] Perfetto E 2006 Phys. Rev. B 74 205123
[23] Dobrescu B E, Pokrovsky V L 2006 Phys. lett. A 350 154
[24] Luo X L, Zhang Z F, Feng M, Fang X M, Gao K L, Zhu X W 1999 Acta Phys. Sin. 48 218 (in Chinese) [罗学立、 张志飞、 冯 芒、 方细明、 高克林、 朱熙文 1999 48 218]
[25] Cherng R W, Levitov L S 2006 Phys. Rev. A 73 043614
[26] Zhang K C, Liu B G 2009 Chin. Phys. B 18 3960
[27] Altman E, Auerbach A 2006 Phys. Rev. Lett. 89 250404
[28] Hackl A, Kehrein S 2008 Phys. Rev. B 78 092303
[29] Hackl A, Kehrein S 2009 J. Phys.: Condens. Matter 21 015601
[30] Stenger J, Inouye S, Stamper-Kum D M, Miesner H J, Chikkatur A P, Ketterle W 1998 Nature 396 345
[31] Chang M S, Hamley C D, Barrett M D, Saner J A, Fortier K M, Zhang W, You L, Chapman M S 2004 Phy. Rev. Lett. 92 140403
[32] Zhao X D, Xie Z W, Zhang W P 2007 Acta Phys. Sin. 56 5358 (in Chinese) [赵兴东、 谢征微、 张卫平 2007 56 5358]
[33] Zheng G P, Liang J Q, Liu W M 2006 Ann. Phys. 321 950
[34] Wang Y J, Liu X F, Han J R 2009 Chin. Phys. B 18 5301
[35] Stein J, 1998, Eur Phys. J. B 5 193
[36] Wang H, Lou P, Zhang Y H 2005 Acta Phys. Sin. 54 3764 (in Chinese) [汪 洪、 娄 平、 庄永河 2005 54 3764]
[37] Wang H, Lou P, Zhang Y H 2004 Acta Phys. Sin. 53 577 (in Chinese) [汪 洪、 娄 平、 庄永河 2004 53 577]
[38] Haldane F D M 1981 J. Phys. C 14 2585
[39] Luther A, Peschel I 1974 Phys. Rev. B 9 2911
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[1] Stamper-Kurn D M, Miesner H J, Chikkatur A P, lnouye S, Stenger J, Ketterle W 1999 Phys. Rev. Lett. 83 661
[2] Wu H Y, Yin L 2006 Acta Phys. Sin. 55 490 (in Chinese) [武宏宇、 尹 澜 2006 55 490]
[3] He Z M, Wang D L, Zhang W X, Wang F J 2008 Chin. Phys. B 17 3640
[4] Chin C, Vuleti’c V, Kerman A J, Chu S 2001 Phys. Rev. Lett. 85 2717
[5] Loftus T, Regal C A, Ticknor C, Bohn J L, Jin D S 2002 Phys. Rev. Lett. 88 173201
[6] Greiner M, Mandel O, Esslinger T, Hnsch T W, Bloch I 2002 Nature 415 39
[7] Barouch E, McCoy B 1970 Phys. Rev. A 2 1075
[8] Stoferle T, Moritz H, Schori C, Kohl M, Esslinger T 2004 Phys. Rev. Lett. 92 130403
[9] Fertig C D, O’Hara K M, Huckans J H, Rolston S L, Phillips W D, Porto J V 2005 Phys. Rev. Lett. 94 120403
[10] Kinoshita T, Wenger T, Weiss D S 2006 Nature 440 900
[11] Zhao J M, Zhang L J, Li C Y, Jia S T 2008 Acta Phys. Sin. 57 2895 (in Chinese) [赵建明、 张临杰、 李昌勇、 贾锁堂 2008 57 2895]
[12] Schreck F Khaykovivh L, Corwin K L, Ferrari G, Bourdel T, Cubizolles J, Salomon C 2001 Phys. Rev. Lett. 87 080403
[13] Strecker K E, Partridge G B, Truscott A G, Hulet R G 2002 Nature 417 150
[14] Jiang Y R, Feng M, Gao K L, Zhu X W 2001 Chin. Phys. 10 202
[15] Calabrese P, Cardy J 2007 J. Stat. Mech. p06008
[16] Wegner F 1994 Ann. Phys. 3 77
[17] Glazek S D, Wilson K G 1994 Phys. Rev. D 49 4214
[18] Kehrein S 2006 The Flow Equation Approach to Many-Particle Systems (Berlin: Springer) p98
[19] Wang F, Zhang F S, Eric S 2003 Chin. Phys. 12 164
[20] Cazalilla M A 2006 Phys. Rev. Lett. 97 156403
[21] Moeckel M, Kehrein S 2008 Phys. Rev. Lett. 100 175702
[22] Perfetto E 2006 Phys. Rev. B 74 205123
[23] Dobrescu B E, Pokrovsky V L 2006 Phys. lett. A 350 154
[24] Luo X L, Zhang Z F, Feng M, Fang X M, Gao K L, Zhu X W 1999 Acta Phys. Sin. 48 218 (in Chinese) [罗学立、 张志飞、 冯 芒、 方细明、 高克林、 朱熙文 1999 48 218]
[25] Cherng R W, Levitov L S 2006 Phys. Rev. A 73 043614
[26] Zhang K C, Liu B G 2009 Chin. Phys. B 18 3960
[27] Altman E, Auerbach A 2006 Phys. Rev. Lett. 89 250404
[28] Hackl A, Kehrein S 2008 Phys. Rev. B 78 092303
[29] Hackl A, Kehrein S 2009 J. Phys.: Condens. Matter 21 015601
[30] Stenger J, Inouye S, Stamper-Kum D M, Miesner H J, Chikkatur A P, Ketterle W 1998 Nature 396 345
[31] Chang M S, Hamley C D, Barrett M D, Saner J A, Fortier K M, Zhang W, You L, Chapman M S 2004 Phy. Rev. Lett. 92 140403
[32] Zhao X D, Xie Z W, Zhang W P 2007 Acta Phys. Sin. 56 5358 (in Chinese) [赵兴东、 谢征微、 张卫平 2007 56 5358]
[33] Zheng G P, Liang J Q, Liu W M 2006 Ann. Phys. 321 950
[34] Wang Y J, Liu X F, Han J R 2009 Chin. Phys. B 18 5301
[35] Stein J, 1998, Eur Phys. J. B 5 193
[36] Wang H, Lou P, Zhang Y H 2005 Acta Phys. Sin. 54 3764 (in Chinese) [汪 洪、 娄 平、 庄永河 2005 54 3764]
[37] Wang H, Lou P, Zhang Y H 2004 Acta Phys. Sin. 53 577 (in Chinese) [汪 洪、 娄 平、 庄永河 2004 53 577]
[38] Haldane F D M 1981 J. Phys. C 14 2585
[39] Luther A, Peschel I 1974 Phys. Rev. B 9 2911
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