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最近一级相变动力学的研究在早期宇宙、致密星体和相对论重离子对撞实验等方面得到了广泛的关注, 特别是与一级相变相关的引力波方面的研究, 是当前宇宙学研究的热点问题. 本文利用有限温度场论, 在有限温度和密度下, 研究了Friedberg-Lee模型下的单圈有效势能和量子色动力学退禁闭相变的动力学机制, 结果表明在全相图中存在一级相变, 在μ = 0 MeV时, 临界温度
$ {T_{\text{c}}} $ = 119.8 MeV; 在T = 50 MeV时, 临界化学势$ {\mu _{\text{c}}} $ = 256.4 MeV. 在薄壁近似下, 通过液滴核合成唯象模型研究了均质气泡成核的强子夸克一级相变的动力学过程, 在适当的边界条件下, 求解场的运动方程, 计算不同温度和密度下气泡临界位形随半径的演化, 获得了表面张力、临界半径和核合成自由能等物理量随温度与夸克化学势密度的变化关系. 为了证明薄壁近似的可靠性和优势, 本文将薄壁近似的分析结果与相应的精确解进行了对比, 讨论了薄壁近似的适用条件, 以及薄壁近似的优缺点等问题. 虽然本文的计算结果是模型相关的, 但是一般性的研发方法和结论具有普适性, 所获得的结果对其他领域一级相变动力学研究有较大的参考价值和现实意义.-
关键词:
- 量子色动力学 /
- Friedberg-Lee模型 /
- 薄壁近似
By using the finite temperature field theory, the one-loop effective potential and the dynamics of the quantum chromodynamics deconfinement phase transition in the framework of Friedberg-Lee model are studied at finite temperature and density. Our results show that there is a first-order deconfinement phase transition for the full phase diagram, and the critical temperature is about 119.8 MeV for a zero chemical potential whereas the critical chemical is around 256.4 MeV when the temperature is fixed at T = 50 MeV. Moreover, in the thin-wall approximation, we investigate the dynamics of a strong first-order quark-hadron transition via homogeneous bubble nucleation in the Friedberg-Lee model. Under an appropriate boundary condition, the equation of motion for the$ \sigma $ field is solved, then the evolutions of the bubble critical configuration with radius$ r $ at different temperatures and densities are calculated. The surface tension, the typical radius of the critical bubble and the shift in the coarse-grained free energy each as a function of temperature and chemical potential are obtained. In order to gain the reliability and advantages of the thin-wall approximation, our analytical results based on the thin-wall approximation are compared with those obtained by the exact numerical method accordingly. Finally, some consequences and possible applications of our results in the quark meson model and Polyakov quark meson model are also presented in the end of this paper.-
Keywords:
- quantum chromodynamics /
- Friedberg-Lee model /
- thin-wall approximation
[1] Fukushima K, Hatsuda T 2011 Rep. Prog. Phys. 74 014001
Google Scholar
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Google Scholar
[3] Nambu Y, Jona-Lasinio G 1961 Phys. Rev. 122 345
Google Scholar
[4] Nambu Y, Jona-Lasinio G 1961 Phys. Rev. 124 246
Google Scholar
[5] Schaefer B J, Pawlowski J M, Wambach J 2007 Phys. Rev. D 76 074023
Google Scholar
[6] Costa P, Ruivo M C, Sousa C D, Hansen H 2010 Symmetry 2 1338
Google Scholar
[7] Coleman S 1977 Phys. Rev. D 15 2929
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Google Scholar
[9] Coleman S 1988 Aspects of Symmetry (Cambridge: Cambridge University Press)
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Google Scholar
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[19] Bessa A, Fraga E S, Mintz B W 2008 Phys. Rev. D 79 034012
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[25] Mao H, Yao M, Zhao W Q 2008 Phys. Rev. C 77 065205
[26] Shu S, Li J R 2010 Phys. Rev. C 82 045203
[27] Birse M C 1992 Progr. Part. Nucl. Phys. 25 1
[28] Laine M, Vuorinen A 2016 Basics of Thermal Field Theory (New York: Springer International Publishing)
[29] Kapusta J I, Gale C 2006 Finite-Temperature Field Theory: Principles and Applications (Cambridge: Cambridge University Press)
[30] Coleman S 1988 Aspects of Symmetry (Cambridge: Cambridge University Press)
[31] Weinberg E J 2012 Classical Solutions in Quantum Field Theory: Solitons and Instantons in High Energy Physics (Cambridge: Cambridge Monographs on Mathematical Physics)
[32] Linde A D 1983 Nucl. Phys. B 216 421 Erratum: [1983 Nucl. Phys. B 223 544]
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图 2 (a)
$ \mu = 0{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ ,$ T = 0, 70, 100, 105, 109{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ 时气泡临界位形; (b)$ T = 50{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ ,$\mu = 0, 150, 200, 230, 240{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}}$ 时气泡临界位形Fig. 2. (a) Bubble critical configuration at
$ \mu = 0{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ ,$ T = 0, 70, 100, 105, 109{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ ; (b) bubble critical configuration at$ T = 50{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ ,$ \mu = 0, 150, 200, 230, 240{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ .
图 3
$ T = {T_{\text{c}}} $ 时表面张力随化学势$ \mu $ 的变化关系Fig. 3. Surface tension as a function of chemical potential
$ \mu $ when$ T = {T_{\text{c}}} $ .
图 4 (a)
$ \mu = 0{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ 时表面张力与温度$ T $ 的关系; (b) T =$ 50{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}}$ 时表面张力与化学势$ \mu $ 的关系Fig. 4. (a) Surface tension as a function of temperature
$ T $ when$ \mu = 0{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ ; (b) surface tension as a function of chemical potential$ \mu $ when$ T = 50{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ .
图 5 (a)
$ \mu = 0{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ 时临界半径与温度$ T $ 的关系; (b)$ T = 50{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ 时临界半径与化学势$ \mu $ 的关系Fig. 5. (a) Typical radius of the critical bubble as a function of temperature
$ T $ when$ \mu = 0{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ ; (b) typical radius of the critical bubble as a function of chemical potential$ \mu $ when$ T = 50{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ .
图 6 (a)
$ \mu = 0{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ 时$ {F_{\text{b}}}/T $ 与温度$ T $ 的关系; (b)$ T = 50{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ 时$ {F_{\text{b}}}/T $ 与化学势$ \mu $ 的关系Fig. 6. (a)
$ {F_{\text{b}}}/T $ as a function of temperature$ T $ when$ \mu = 0{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ ; (b)$ {F_{\text{b}}}/T $ as a function of chemical potential$ \mu $ when$ T = 50{\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\kern 1 pt} {\text{MeV}} $ . -
[1] Fukushima K, Hatsuda T 2011 Rep. Prog. Phys. 74 014001
Google Scholar
[2] Gell-Mann M, Levy M 1960 Nuovo. Cimento. 16 705
Google Scholar
[3] Nambu Y, Jona-Lasinio G 1961 Phys. Rev. 122 345
Google Scholar
[4] Nambu Y, Jona-Lasinio G 1961 Phys. Rev. 124 246
Google Scholar
[5] Schaefer B J, Pawlowski J M, Wambach J 2007 Phys. Rev. D 76 074023
Google Scholar
[6] Costa P, Ruivo M C, Sousa C D, Hansen H 2010 Symmetry 2 1338
Google Scholar
[7] Coleman S 1977 Phys. Rev. D 15 2929
[8] Callan C G, Coleman J, Coleman S 1977 Phys. Rev. D 16 1762
Google Scholar
[9] Coleman S 1988 Aspects of Symmetry (Cambridge: Cambridge University Press)
[10] Linde A D 1981 Phys. Lett. B 100B 37
[11] Linde A D 1983 Nucl. Phys. B 216 421
Google Scholar
[12] Kohsuke Y, Tetsuo H, Yasuo M 2005 Quark-Gluon Plasma (Cambridge: Cambridge University Press)
[13] Friedberg R, Lee T D 1977 Phys. Rev. D 15 1694
Google Scholar
[14] Friedberg R, Lee T D 1977 Phys. Rev. D 16 1096
Google Scholar
[15] Friedberg R, Lee T D 1978 Phys. Rev. D 18 2623
Google Scholar
[16] Daniel C, Mark H, Weir D J 2018 Phys. Rev. D 97 123513
Google Scholar
[17] Cutting D, Escartin E G, Hindmarsh M, Weir D J 2021 Phys. Rev. D 103 023531
[18] Wang X, Huang F P, Zhang X 2020 JCAP 2005 045
[19] Bessa A, Fraga E S, Mintz B W 2008 Phys. Rev. D 79 034012
[20] Zhou S, Shu S, Mao H 2021 Chin. Phys. C 45 043104
Google Scholar
[21] Goldflam R, Wilets L 1982 Phys. Rev. D 25 1951
Google Scholar
[22] Reinhardt H, Dang B V, Schulz H 1985 Phys. Lett. B 159 161
Google Scholar
[23] Li M, Birse M C, Wilets L 1987 J. Phys. G 13 1
Google Scholar
[24] Gao S, Wang E, Jiarong L I 1992 Phys. Rev. D 46 3211
Google Scholar
[25] Mao H, Yao M, Zhao W Q 2008 Phys. Rev. C 77 065205
[26] Shu S, Li J R 2010 Phys. Rev. C 82 045203
[27] Birse M C 1992 Progr. Part. Nucl. Phys. 25 1
[28] Laine M, Vuorinen A 2016 Basics of Thermal Field Theory (New York: Springer International Publishing)
[29] Kapusta J I, Gale C 2006 Finite-Temperature Field Theory: Principles and Applications (Cambridge: Cambridge University Press)
[30] Coleman S 1988 Aspects of Symmetry (Cambridge: Cambridge University Press)
[31] Weinberg E J 2012 Classical Solutions in Quantum Field Theory: Solitons and Instantons in High Energy Physics (Cambridge: Cambridge Monographs on Mathematical Physics)
[32] Linde A D 1983 Nucl. Phys. B 216 421 Erratum: [1983 Nucl. Phys. B 223 544]
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