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在Nambu−Jona-Lasinio模型框架下, 研究温度和重子化学势对同位旋非对称量子色动力学物质状态方程和热力学性质的影响. 通过将零温和零重子化学势下的pion超流物质状态方程以及有限温下同位旋密度、压强与格点数据做比较, 发现两种方法给出的结果符合得较好. 进一步计算表明, 零温和零重子化学势下的平均同位旋能量随同位旋密度单调增加, 而非零重子化学势和有限温下却呈现具有极小值的非对称抛物线行为. 最后, 利用得到的状态方程探讨声速随同位旋化学势的变化行为, 结果显示有限温和(或)重子化学势下的声速在相变点不连续, 且超流相中的声速饱和值明显大于普通核物质及夸克物质中的值. 另外, 在超流相中重子化学势和温度具有软化状态方程以及降低声速的作用.The effects of temperature and baryon chemical potential on equation of state and thermodynamics of isospin imbalanced QCD matter are investigated in the framework of two-flavor Nambu−Jona-Lasinio model. The equation of state at zero temperature and baryon chemical potential as well as the isospin density and normalized pressure at finite temperature are shown to be consistent with the lattice data. We also find that the energy per isospin increases monotonically with the increase of isospin density at vanishing temperature and baryon chemical potential, while it first decreases and then increases with the augment of isospin density, behaving as a non-symmetric parabolic curve. Finally, we compute the sound velocity and find that it is discontinuous at the phase transition point for finite temperature and/or baryon chemical potential. In particular, the sound velocity in the superfluid phase is distinctly larger than that in the ordinary nuclear matter and quark matter, while the temperature and baryon chemical potential included in the superfluid phase makes the equation of state softer and the sound velocity slower.
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Keywords:
- isospin chemical potential /
- Bose-Einstein condensation /
- second order phase transition /
- thermodynamics
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图 1 温度
$T=0.124$ GeV时, 归一化同位旋密度$n_{\rm I}/T^3$ (上板面) 和归一化压强$\Delta P/T^4$ (下板面) 随同位旋化学势的变化关系. 蓝色实心圆表示取自文献[54]的格点数据Fig. 1. Normalized isospin density
$n_{\rm I}/T^3$ (upper panel) and normalized pressure$\Delta P/T^4$ (lower panel) as functions of$\mu_{\rm I}/m_\pi$ at fixed$T=0.124$ GeV. The blue circles are taken from Ref.[54] for comparison. -
[1] Graf T, Schaffner-Bielich J, Fraga E S 2016 Phys. Rev. D 93 085030Google Scholar
[2] Xu J F, Peng G X, Lu Z Y, Cui S S 2015 Sci. China Phys. Mech. Astron. 58 042001Google Scholar
[3] Xu J F, Peng G X, Liu F, Hou D F, Chen L W 2015 Phys. Rev. D 92 025025Google Scholar
[4] Allton C, Ejiri S, Hands S, Kaczmarek O, Karsch F, Laermann E, Schmidt C 2003 Phys. Rev. D 68 014507Google Scholar
[5] Borsanyi S, Endrodi G, Fodor Z, Katz S D, Krieg S, Ratti C, Szabo K K 2012 JHEP 08 053Google Scholar
[6] Bazavov A, Ding H T, Hegde P, Kaczmarek O, Karsch F, Laermann E, Maezawa Y, Mukherjee S, Ohno H, Petreczky P, Sandmeyer H, Steinbrecher P, Schmidt C, Sharma S, Soeldner W, Wagner M 2017 Phys. Rev. D 95 054504Google Scholar
[7] Gasser J, Leutwyler H 1985 Nucl. Phys. B 250 465Google Scholar
[8] Balkin R, Serra J, Springmann K, Weiler A 2020 JHEP 07 221Google Scholar
[9] Nambu Y, Jona-Lasinio G 1961 Phys. Rev. 122 345Google Scholar
[10] Nambu Y, Jona-Lasinio G 1961 Phys. Rev. 124 246Google Scholar
[11] Hatsuda T, Kunihiro T 1994 Phys. Rep. 247 221Google Scholar
[12] Schaefer B J, Pawlowski J M, Wambach J 2007 Phys. Rev. D 76 074023Google Scholar
[13] Li X, Fu W J, Liu Y X 2019 Phys. Rev. D 99 074029Google Scholar
[14] 沈婉萍, 尤仕佳, 毛鸿 2019 物理学报 68 181101Google Scholar
Shen W P, You S J, Mao H 2019 Acta Phys. Sin. 68 181101Google Scholar
[15] Xu S S, Cui Z F, Wang B, Shi Y M, Yang Y C, Zong H S 2015 Phys. Rev. D 91 056003Google Scholar
[16] Gao F, Liu Y X 2016 Phys. Rev. D 94 094030Google Scholar
[17] Contant R, Huber M Q 2020 Phys. Rev. D 101 014016Google Scholar
[18] Peng G X, Chiang H C, Yang J J, Li L, Liu B 2000 Phys. Rev. C 61 015201Google Scholar
[19] Wen X J, Zhong X H, Peng G X, Shen P N, Ning P Z 2005 Phys. Rev. C 72 015204Google Scholar
[20] Xia C J, Peng G X, Chen S W, Lu Z Y, Xu J F 2014 Phys. Rev. D 89 105027Google Scholar
[21] Chu P C, Chen L W 2014 Astrophys. J. 780 135Google Scholar
[22] Chu P C, Zhou Y, Li X H, Zhang Z 2019 Phys. Rev. D 100 103012Google Scholar
[23] Peshier A, Kampfer B, Soff G 2000 Phys. Rev. C 61 045203Google Scholar
[24] Wen X J, Feng Z Q, Li N, Peng G X 2009 J. Phys. G 36 025011Google Scholar
[25] Cao J, Jiang Y, Sun W M, Zong H S 2012 Phys. Lett. B 711 65Google Scholar
[26] Son D T, Stephanov M A 2001 Phys. Rev. Lett. 86 592Google Scholar
[27] Kogut J B, Sinclair D K 2002 Phys. Rev. D 66 034505Google Scholar
[28] Kogut J B, Sinclair D K 2002 Phys. Rev. D 66 014508Google Scholar
[29] Kogut J B, Sinclair D K 2004 Phys. Rev. D 70 094501Google Scholar
[30] He L Y, Jin M, Zhuang P F 2005 Phys. Rev. D 71 116001Google Scholar
[31] He L Y, Jin M, Zhuang P F 2005 Phys. Lett. B 615 93Google Scholar
[32] Warringa H J, Boer D, Andersen J O 2005 Phys. Rev. D 72 014015Google Scholar
[33] Adhikari P, Andersen J O, Kneschke P 2019 Eur. Phys. J. C 79 874Google Scholar
[34] Adhikari P, Andersen J O 2020 JHEP 06 170Google Scholar
[35] Wu Z, Ping J, Zong H 2017 Chin. Phys. C 41 124106Google Scholar
[36] Xiong J, Jin M, Li J 2009 J. Phys. G 36 125005Google Scholar
[37] Xia T, He L, Zhuang P 2013 Phys. Rev. D 88 056013Google Scholar
[38] Mammarella A, Mannarelli M 2015 Phys. Rev. D 92 085025Google Scholar
[39] Mao S 2014 Phys. Rev. D 89 116006Google Scholar
[40] Brandt B B, Endrodii G, Fraga E S, Hippert M, Schaffner-Bielich J, Schmalzbauer S 2018 Phys. Rev. D 98 094510Google Scholar
[41] Chao J, Huang M, Radzhabov A 2020 Chin. Phys. C 44 034105Google Scholar
[42] Mannarelli M 2019 Particles 2 411Google Scholar
[43] Lu Z Y, Xia C J, Ruggieri M 2020 Eur. Phys. J. C 80 46Google Scholar
[44] Gatto R, Ruggieri M 2012 Phys. Rev. D 85 054013Google Scholar
[45] Borsanyi S, Fodor Z, Guenther J, Kampert K H, Katz S D, Kawanai T, Kovacs T G, Mages S W, Pasztor A, Pittler F, Redondo J, Ringwald A, Szabo K K 2016 Nature 539 69Google Scholar
[46] Lu Z Y, Du M L, Guo F K, Meißner U G, Vonk T 2020 JHEP 05 001Google Scholar
[47] Grilli C G, Hardy E, Pardo V J, Villadoro G 2016 JHEP 01 034Google Scholar
[48] Lu Z Y, Ruggieri M 2019 Phys. Rev. D 100 014013Google Scholar
[49] 李昂, 胡金牛, 鲍世绍, 申虹, 徐仁新 2019 原子核物理评论 36 1Google Scholar
Li A, Hu J N, Bao S S, Shen H, Xu R X 2019 Nucl. Phys. Rev. 36 1Google Scholar
[50] Gorenstein M I, Yang S N 1995 Phys. Rev. D 52 5206Google Scholar
[51] Lu Z Y, Peng G X, Xu J F, Zhang S P 2016 Sci. China Phys. Mech. Astron. 59 662001Google Scholar
[52] Wen X J, Su S Z, Yang D H, Peng G X 2012 Phys. Rev. D 86 034006Google Scholar
[53] Zhuang P, Hufner J, Klevansky S P 1994 Nucl. Phys. A 576 525Google Scholar
[54] Brandt B B, EndrHodi G, Schmalzbauer S 2018 EPJ Web Conf. 175 07020Google Scholar
[55] Avancini S S, Bandyopadhyay A, Duarte D C, Farias R L S 2019 Phys. Rev. D 100 116002Google Scholar
[56] Farhi E, Jaffe R L 1984 Phys. Rev. D 30 2379Google Scholar
[57] Lu Z Y, Peng G X, Zhang S P, Ruggieri M, Greco V 2016 Nucl. Sci. Tech. 27 148Google Scholar
[58] Carignano S, Lepori L, Mammarella A, Mannarelli M, Pagliaroli G 2017 Eur. Phys. J. A 53 35Google Scholar
[59] Di Clemente F, Mannarelli M, Tonelli F 2020 Phys. Rev. D 101 103003Google Scholar
[60] Demorest P, Pennucci T, Ransom S, Roberts M, Hessels J 2010 Nature 467 1081Google Scholar
[61] Antoniadis J, Freire P, Wex N, et al. 2013 Science 340 6131Google Scholar
[62] Linares M, Shahbaz T, Casares J 2018 Astrophys. J. 859 54Google Scholar
[63] Cromartie H T, Fonseca E, Ransom S M, et al. 2019 Nature Astron. 4 72Google Scholar
[64] Reed B, Horowitz C 2020 Phys. Rev. C 101 045803Google Scholar
[65] Carignano S, Mammarella A, Mannarelli M 2016 Phys. Rev. D 93 051503Google Scholar
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