近平衡态下QGP中成分粒子的分布函数研究
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摘要
QGP物理是当今物理学前沿的重要研究领域。探测QGP这种新的物质形态是新一代高能物理实验(RHIC和LHC)的一个重要目标。有关QGP的产生和演化机制，人们己进行了许多探讨。通常认为在相对论重离子碰撞中生成的QGP首先是处于非平衡态，它要经过一个由非平衡态向平衡态演化的驰豫过程。如何描述QGP的非平衡态一直是尚未解决的关键问题。
讨论QGP的非平衡效应所要用到的两个最基本的理论框架是有限温度场论和动力论。其中，动力论是在统计物理框架内描述系统中非平衡现象的基本理论。QGP动力论的基本方程是以系统的成分粒子(夸克、反夸克和胶子)所服从的QCD为动力学基础，按统计理论的一般框架建立起来的，现已广泛应用于讨论QGP的物性，并已证实在“硬热圈”水平上动力论和温度场论的结果是一致的，因而该理论得到普遍的承认。
QGP的动力论有两种基本形式：量子动力论和(半)经典动力论。目前运用得较为成功的是(半)经典动力论。即使从QGP动力论出发，由于其非线性和非阿贝尔性导致系统处于非平衡态的机制很复杂，直接得到完整的解析解比较困难，必须尝试可用的近似求解方法。
动力论方法是用相空间分布函数来实现对系统的统计描述。分布函数描述系统中任一粒子在坐标空间和动量空间的分布。实际中分布函数主要被用来求各种观测量的期待值和相关函数，因为这些正是我们在实验中测量和热力学中讨论的量。对于一个经典系统，知道了分布函数，宏观物理量就可以用分布函数的矩表示。在相对论重离子碰撞中生成的QGP首先是处于非平衡态，生成的QGP要经过一个向平衡态演化的过程。因此给出QGP非平衡态下的分布函数是描述QGP非平衡态的关键问题。
JtwA硕士学位论文
W一步M仅盯E厂 S T IESIS
本篇论文的工作就是研究近平衡态下QGP成分粒子分布函数的特
性。主要讨论了两个方面的问题。第一，从QGP动力论出发，忽略自
旋和碰撞效应，得到QGP在色场涨落扰动下偏离平衡态而处于近平衡时
的分布函数的二级近似以及偏离因子的物理表示，进而分析了决定偏
离因子的物理因素。并分别讨论了在两种有特别物理兴趣情况下（高
温低密和低温高密区广偏离因子特征。结果表明，对于高温低化学势
区，在。二丁（Inl．86481）十 p时，而对于低温高化学势区，在费米面附近
拍。。…的夸克和反夸克在色场涨落扰动下偏离平衡较远。第二，从有
碰撞项的QGP动力论方程出发，忽略自旋，在色涨落扰动下，利用弛豫时
间近似，得到夸克和胶子分布函数的二级修正，通过数值分析重点讨论了
高温低密情况下QGP中成分粒子分布函数的特性，并且由分布函数得到净
重子数密度和能量密度。结果表明重子数密度和能量密度与高能重离子碰
撞实验的唯象分析有关。
One of the main objectives of the future high-energy experiments is to detect a new state of matter called the quark-gluon plasma (QGP). Considerable attention has been paid on the mechanism of the formation and the evolution of the QGP. It's generally believed that the QGP, if formed in the relativistic heavy ion collisions, be in a thermal non-equilibrium state during initial stage and then evaluates into equilibrium state. However, how to describe the non-equilibrium state of QGP is still an unsolved and important problem.
The fundamental theoretic methods dealing with the phenomenon of the QGP in non-equilibrium are the finite-temperature field theory and the kinetic theory. The kinetic theory is a statistical theory that can describe the non-equilibrium phenomena in basic. The kinetic equations for the QGP have been formed under the general frame of the statistical theory and its dynamic basic is the quantum chromodynamics(QCD), which the component particles of the system obey. They are widely used in investigating the properties of the QGP.
There are two basic forms of the QGP kinetic theory: quantum kinetic theory and (semi-)classical kinetic theory. Unfortunately, it is difficult to obtain the non-equilibrium distribution functions by strictly solving the QGP kinetic equations.
Here based on the kinetic theory, we have mainly discussed the distribution function of the component particles in QGP which is in quasi-
equilibrium. Our discussion can be divided into two aspects. The first aspect is about the distribution function for fermions in quasi-equilibrium QGP which is perturbed by the fluctuation of the color field. Neglecting the affect of the spin and the collision between the particles in QGP, the distribution function for fermions in quasi-equilibrium QGP has been obtained. Further more, the physical' basses that decide the departure factor are analyzed. And the characteristics of the departure factor in high-temperature-low-density and low-temperature-high-density are discussed. The second aspect: from QGP kinetic equations with collision integrals, by using the relaxation time approximation, we calculate the distribution functions to the second order correction. We obtain the distribution functions for quarks(and anti-quarks)and gluons under perturbation of the fluctuation of the color field. Then in the high-temperature-low-density area, we discuss the characteristics of the distribution functions, and use t
hem to get the net baryon density and the energy density.
讨论QGP的非平衡效应所要用到的两个最基本的理论框架是有限温度场论和动力论。其中，动力论是在统计物理框架内描述系统中非平衡现象的基本理论。QGP动力论的基本方程是以系统的成分粒子(夸克、反夸克和胶子)所服从的QCD为动力学基础，按统计理论的一般框架建立起来的，现已广泛应用于讨论QGP的物性，并已证实在“硬热圈”水平上动力论和温度场论的结果是一致的，因而该理论得到普遍的承认。
QGP的动力论有两种基本形式：量子动力论和(半)经典动力论。目前运用得较为成功的是(半)经典动力论。即使从QGP动力论出发，由于其非线性和非阿贝尔性导致系统处于非平衡态的机制很复杂，直接得到完整的解析解比较困难，必须尝试可用的近似求解方法。
动力论方法是用相空间分布函数来实现对系统的统计描述。分布函数描述系统中任一粒子在坐标空间和动量空间的分布。实际中分布函数主要被用来求各种观测量的期待值和相关函数，因为这些正是我们在实验中测量和热力学中讨论的量。对于一个经典系统，知道了分布函数，宏观物理量就可以用分布函数的矩表示。在相对论重离子碰撞中生成的QGP首先是处于非平衡态，生成的QGP要经过一个向平衡态演化的过程。因此给出QGP非平衡态下的分布函数是描述QGP非平衡态的关键问题。
JtwA硕士学位论文
W一步M仅盯E厂 S T IESIS
本篇论文的工作就是研究近平衡态下QGP成分粒子分布函数的特
性。主要讨论了两个方面的问题。第一，从QGP动力论出发，忽略自
旋和碰撞效应，得到QGP在色场涨落扰动下偏离平衡态而处于近平衡时
的分布函数的二级近似以及偏离因子的物理表示，进而分析了决定偏
离因子的物理因素。并分别讨论了在两种有特别物理兴趣情况下（高
温低密和低温高密区广偏离因子特征。结果表明，对于高温低化学势
区，在。二丁（Inl．86481）十 p时，而对于低温高化学势区，在费米面附近
拍。。…的夸克和反夸克在色场涨落扰动下偏离平衡较远。第二，从有
碰撞项的QGP动力论方程出发，忽略自旋，在色涨落扰动下，利用弛豫时
间近似，得到夸克和胶子分布函数的二级修正，通过数值分析重点讨论了
高温低密情况下QGP中成分粒子分布函数的特性，并且由分布函数得到净
重子数密度和能量密度。结果表明重子数密度和能量密度与高能重离子碰
撞实验的唯象分析有关。
One of the main objectives of the future high-energy experiments is to detect a new state of matter called the quark-gluon plasma (QGP). Considerable attention has been paid on the mechanism of the formation and the evolution of the QGP. It's generally believed that the QGP, if formed in the relativistic heavy ion collisions, be in a thermal non-equilibrium state during initial stage and then evaluates into equilibrium state. However, how to describe the non-equilibrium state of QGP is still an unsolved and important problem.
The fundamental theoretic methods dealing with the phenomenon of the QGP in non-equilibrium are the finite-temperature field theory and the kinetic theory. The kinetic theory is a statistical theory that can describe the non-equilibrium phenomena in basic. The kinetic equations for the QGP have been formed under the general frame of the statistical theory and its dynamic basic is the quantum chromodynamics(QCD), which the component particles of the system obey. They are widely used in investigating the properties of the QGP.
There are two basic forms of the QGP kinetic theory: quantum kinetic theory and (semi-)classical kinetic theory. Unfortunately, it is difficult to obtain the non-equilibrium distribution functions by strictly solving the QGP kinetic equations.
Here based on the kinetic theory, we have mainly discussed the distribution function of the component particles in QGP which is in quasi-
equilibrium. Our discussion can be divided into two aspects. The first aspect is about the distribution function for fermions in quasi-equilibrium QGP which is perturbed by the fluctuation of the color field. Neglecting the affect of the spin and the collision between the particles in QGP, the distribution function for fermions in quasi-equilibrium QGP has been obtained. Further more, the physical' basses that decide the departure factor are analyzed. And the characteristics of the departure factor in high-temperature-low-density and low-temperature-high-density are discussed. The second aspect: from QGP kinetic equations with collision integrals, by using the relaxation time approximation, we calculate the distribution functions to the second order correction. We obtain the distribution functions for quarks(and anti-quarks)and gluons under perturbation of the fluctuation of the color field. Then in the high-temperature-low-density area, we discuss the characteristics of the distribution functions, and use t
hem to get the net baryon density and the energy density.
引文
1. J. Collins and M. Perry, Phys. Rev. Lett. 34, 135(1975).
2. E. V. Shuryak, The QCD Vacuum, hadrons and Super Dense Matter (World Scientific, Singapore, 1988).
3. E. V. Shuryak, Phys. Rep 61, 71(1980); Phys. Rep 115, 151(1984).
4. R. C. Hwa ed., Quark-Gluon Plasma (World Scientific, Singapore, 1990); Quark-Gluon Plasma 2 (World Scientific, Singapore, 1995).
5. K. A. Olive, Science 251, 1194(1991).
6. N. K. Glendenning, Phys. Rev. D46, 1274; H. Heiselberg, C. J. Pethick and E. F. Staubo, Phys. Rev. Lett. 70, 1355(1993).
7. V. A. Rubakov and M. E. Shaposhnikov, Usp. Fiz. Nauk. 166, 493(1996).
8. K. Rummukainen, M. Tyspin, K. Kajantie, M.Laine and M. E. Shaposhnikov, Nucl. Phys. B532, 283(1998).
9. A. Linde, Particle Physics and Inflationary Cosmology (Harwood, Phi; ade; phia, 1990).
10. B. Sinha ed., Physics and Astrophysics of Quark-Gluon Plasma (World Scientific, Singapore, 1989).
11. H. Satz ed., Thermodynamics of Quarks and Hadrons (North Holland,Amsterdam, 1981).
12. T. W. Ludlam and H. E. Wagner ed., Quark Matter'83 Nucl. Phys. A418(1984); K. Kajantie ed., Quark Matter'84 Lecture Notes in Physics 221 (Springer Verlag,Berlin/New York,1985).
13. B. Müller, The Physics of the Quark-Gluon Plasma,Lecture Notes in Physics 225 (Springer Verlag,Berlin/New York, 1985).
14．李家荣，《夸克物质理论导论》，湖南教育出版社，1989年．
15. J. D. Bjorken, Phys. Rev. D27, 140(1983).
16. K. Kajantie and L. Mclerrn, Ann. Rev. Nuci. Sci. 37, 293(1987).
17. V. Bernard ed., et al. QGP Signature (Editions Fronti(?)res, Parise, 1990).
18. B. Muller, Nucl. Phys. A544, 95(1992).
19. H. -Th. Elze and Heinz, Phys. Rep. C183, 81(1989).
20. J. I. Kapusta, Finite Temperature Field Theory (Cambridge University Press, 1989).
21. A. Das, Finite Temperature Field Theory (World Scientific, Singapore, 1997).
22. M. Le Bellec, Thermal Field THeory (Cambridge Press, 1996).
23. E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics (Pergamon, Oxford, 1981).
24. U. Heinz, Phys. Rev. Lett. 51, 351(1983); U. Heinz, Ann. Phys.161, 48(1985).
25. S. Mrówczy(?)ski, hep-ph/9805435.
26. J. -P. Blaizot, E. Iancu and A. Rebhan, Phys. Rev. Lett. 83, 2906(1999); Phys. Lett. B470, 181(1999).
27. H.-Th. Elze, Z.Phys. C38, 211(1988).
28. S. R. de Groot, W. A. van leeeuwen and C. G. van Weert, Relativistic Kinetic Theory (North Holland,Amsterdam,1981).
29. P. Carruthers and F. Zachariasen, Rev. Mod. Phys. 55, 245(1983).
30. R. Blaescu, Equilibrium and Non-Equilibriurn Statistical Mechanics (Wiley, New York, 1975).
31. J. -P. Blaizot and E. Iancu, Phys. Rev. Lett. 70, 3376(1993).
32. S. Mrówczy(?)ski, Phys. Rev. D39, 1940(1989).
33. J. -P. Blaizot and E. Iancu, Nucl. Phys. B417, 608(1994).
34. U. Heinz, K. Kajantie and T. Toimela, Ann. Phys.176, 218(1987).
35. Zhang Xiaofei and Li Jiarong, Phys. Rev. C52, 964(1995).
36. Y. A.Markov and R. A. Markova, Transp. Theory Statist. Phys.28, 645(1999).
37. L. W. Nordheim, Proc. Roy. Soc. A119, 689(London, 1928).
38. E. A. Uehling and G. E. Uhlenbeck, Phys. Rep 43552. 2891(1993); Phys. Rev. D47, 5601(1993).
39. Y. Nambu, Prog. Theory. Phys.5, 82(1950).
40. H. -Th. Elze, M. Gyulassy and D. Vasak, Nucl. Phys. B276, 706(1986).
41. H. -Th. Elze, M. Gyulassy and D. Vasak, Nucl. Phys. B177,402(1986).
42. S. Mrówczy(?)ski, Phys. Rev. D39, 1940(1989).
43. U. Heinz, Phys. A158, 111(1989).
44. K. J. Eskola and X. N. Wang, Phys. Rev. D49, 1284(1994).
45. D.B(?)deker, Phys. Rev. B426, 351(1998); Nucl. Phys. B570, 326(2000).
46. P. Anold, D. Son, L. G. Yaffe, Phys. Rev. D59, 105020(1999); Phys. Rev. D60, 025007(1999).
47. J. P. Blaizot and E.Iancu, Nucl. Phys. B557, 183(1999); J.P. Blaizot, E.Iancu, Nucl. Phys. B570, 326(2000).
48. P. F. Kelly, Q. LIU and C. Lucchesi et al., Phys. Rev. Lett. 72, 3461(1994).
49. Zhang Xiaofei and Li Jiarong, Ann. Phys(N.Y)250, 433(1996).
50. Yang Fang, Zhou Yunqing and Li Jiarong, 《高能物理与核物理》 27(1), 58(2003).
51. Hou Defu and Li Jiarong, Nucl. phys. A618, 371(1997).
52. Zhou Yunqing, Yang Fang and Li Jiarong, High Energy Physics and Nuclear Physics (待发) .
2. E. V. Shuryak, The QCD Vacuum, hadrons and Super Dense Matter (World Scientific, Singapore, 1988).
3. E. V. Shuryak, Phys. Rep 61, 71(1980); Phys. Rep 115, 151(1984).
4. R. C. Hwa ed., Quark-Gluon Plasma (World Scientific, Singapore, 1990); Quark-Gluon Plasma 2 (World Scientific, Singapore, 1995).
5. K. A. Olive, Science 251, 1194(1991).
6. N. K. Glendenning, Phys. Rev. D46, 1274; H. Heiselberg, C. J. Pethick and E. F. Staubo, Phys. Rev. Lett. 70, 1355(1993).
7. V. A. Rubakov and M. E. Shaposhnikov, Usp. Fiz. Nauk. 166, 493(1996).
8. K. Rummukainen, M. Tyspin, K. Kajantie, M.Laine and M. E. Shaposhnikov, Nucl. Phys. B532, 283(1998).
9. A. Linde, Particle Physics and Inflationary Cosmology (Harwood, Phi; ade; phia, 1990).
10. B. Sinha ed., Physics and Astrophysics of Quark-Gluon Plasma (World Scientific, Singapore, 1989).
11. H. Satz ed., Thermodynamics of Quarks and Hadrons (North Holland,Amsterdam, 1981).
12. T. W. Ludlam and H. E. Wagner ed., Quark Matter'83 Nucl. Phys. A418(1984); K. Kajantie ed., Quark Matter'84 Lecture Notes in Physics 221 (Springer Verlag,Berlin/New York,1985).
13. B. Müller, The Physics of the Quark-Gluon Plasma,Lecture Notes in Physics 225 (Springer Verlag,Berlin/New York, 1985).
14．李家荣，《夸克物质理论导论》，湖南教育出版社，1989年．
15. J. D. Bjorken, Phys. Rev. D27, 140(1983).
16. K. Kajantie and L. Mclerrn, Ann. Rev. Nuci. Sci. 37, 293(1987).
17. V. Bernard ed., et al. QGP Signature (Editions Fronti(?)res, Parise, 1990).
18. B. Muller, Nucl. Phys. A544, 95(1992).
19. H. -Th. Elze and Heinz, Phys. Rep. C183, 81(1989).
20. J. I. Kapusta, Finite Temperature Field Theory (Cambridge University Press, 1989).
21. A. Das, Finite Temperature Field Theory (World Scientific, Singapore, 1997).
22. M. Le Bellec, Thermal Field THeory (Cambridge Press, 1996).
23. E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics (Pergamon, Oxford, 1981).
24. U. Heinz, Phys. Rev. Lett. 51, 351(1983); U. Heinz, Ann. Phys.161, 48(1985).
25. S. Mrówczy(?)ski, hep-ph/9805435.
26. J. -P. Blaizot, E. Iancu and A. Rebhan, Phys. Rev. Lett. 83, 2906(1999); Phys. Lett. B470, 181(1999).
27. H.-Th. Elze, Z.Phys. C38, 211(1988).
28. S. R. de Groot, W. A. van leeeuwen and C. G. van Weert, Relativistic Kinetic Theory (North Holland,Amsterdam,1981).
29. P. Carruthers and F. Zachariasen, Rev. Mod. Phys. 55, 245(1983).
30. R. Blaescu, Equilibrium and Non-Equilibriurn Statistical Mechanics (Wiley, New York, 1975).
31. J. -P. Blaizot and E. Iancu, Phys. Rev. Lett. 70, 3376(1993).
32. S. Mrówczy(?)ski, Phys. Rev. D39, 1940(1989).
33. J. -P. Blaizot and E. Iancu, Nucl. Phys. B417, 608(1994).
34. U. Heinz, K. Kajantie and T. Toimela, Ann. Phys.176, 218(1987).
35. Zhang Xiaofei and Li Jiarong, Phys. Rev. C52, 964(1995).
36. Y. A.Markov and R. A. Markova, Transp. Theory Statist. Phys.28, 645(1999).
37. L. W. Nordheim, Proc. Roy. Soc. A119, 689(London, 1928).
38. E. A. Uehling and G. E. Uhlenbeck, Phys. Rep 43552. 2891(1993); Phys. Rev. D47, 5601(1993).
39. Y. Nambu, Prog. Theory. Phys.5, 82(1950).
40. H. -Th. Elze, M. Gyulassy and D. Vasak, Nucl. Phys. B276, 706(1986).
41. H. -Th. Elze, M. Gyulassy and D. Vasak, Nucl. Phys. B177,402(1986).
42. S. Mrówczy(?)ski, Phys. Rev. D39, 1940(1989).
43. U. Heinz, Phys. A158, 111(1989).
44. K. J. Eskola and X. N. Wang, Phys. Rev. D49, 1284(1994).
45. D.B(?)deker, Phys. Rev. B426, 351(1998); Nucl. Phys. B570, 326(2000).
46. P. Anold, D. Son, L. G. Yaffe, Phys. Rev. D59, 105020(1999); Phys. Rev. D60, 025007(1999).
47. J. P. Blaizot and E.Iancu, Nucl. Phys. B557, 183(1999); J.P. Blaizot, E.Iancu, Nucl. Phys. B570, 326(2000).
48. P. F. Kelly, Q. LIU and C. Lucchesi et al., Phys. Rev. Lett. 72, 3461(1994).
49. Zhang Xiaofei and Li Jiarong, Ann. Phys(N.Y)250, 433(1996).
50. Yang Fang, Zhou Yunqing and Li Jiarong, 《高能物理与核物理》 27(1), 58(2003).
51. Hou Defu and Li Jiarong, Nucl. phys. A618, 371(1997).
52. Zhou Yunqing, Yang Fang and Li Jiarong, High Energy Physics and Nuclear Physics (待发) .