Criterion for reducible hydrodynamic equations of baryon-rich quark-gluon plasma

Criterion for reducible hydrodynamic equations of baryon-rich quark-gluon plasma 1 2 first-author Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000 Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000 Shanghai Institute of Nuclear Research, the Chinese Academy of Sciences, Shanghai 201800 Shanghai Institute of Nuclear Research, the Chinese Academy of Sciences, Shanghai 201800 Besides the state equation there exists another cubic algebraic equation about μf in the form of <math><mrow><msubsup><mi>μ</mi><mi>f</mi><mn>3</mn></msubsup></mrow></math> + pμf + q = 0, which relates parameters, temperature T , chemical potential μf, and net quark number nff (flavor f ) for a baryon-rich quark-gluon plasma (QGP). A criterion may be acquired simply according to Cardan formula of the solution of the above equation, which gives naturally a condition: if n <math><mrow><mo>≪</mo><mn>2</mn><mi>π</mi><msup><mi>T</mi><mn>3</mn></msup><mo>/</mo><mn>3</mn><msqrt><mn>3</mn></msqrt></mrow></math> , one may approximately use the conservation of specific entropy, and then the set of hydrodynamic equation of baryon-rich QGP may be reduced to the set of hydrodynamic equation for baryon-free QGP. Space-time evolution Baryon-rich quark-gluon plasma Cardan formula References Busza W. Nucl Phys , 1984 , A418 : 635c Nucl Phys Bolz J , Ornik U , Weiner R M. Phys Rev , 1992 , C46 : 2047 Phys Rev Barrette J. Phys Lett , 1994 , B333 : 33 Phys Lett Åkesson T et al . Z Phys , 1988 , C38 : 383 Z Phys Danos M , Rafelski J. Baryon-rich quark-gluon plasma in nuclear collisions UCT-TPT/84 Baryon-rich quark-gluon plasma in nuclear collisions UCT-TPT/84 He Z J , Zhang J J. J Phys , 1995 , G21 : L49 J Phys Ko C M , Xia L H. Phys Rev Lett , 1989 , 62 : 1595 Phys Rev Lett He Z J , Zhang J J , Li P L. Nucl Phys , 1991 A532 : 743 Nucl Phys Koch P , Müller B , Rafelski J. Phys Rep , 1986 , 142 : 167 Phys Rep Kajantie K , Miettinen H. Z Phys , 1981 , C9 : 341 Z Phys Clausius R . A source book in physics , Magie William F ed. 1935 , 235 . A source book in physics Ai H B. in: Proceedings of the Fourth Pacific Physics Conference , Ahn S H et al Ed. Seoul . August 13-17, 1990 ( Singapore : World Scientific , 1991 ) Vol.1 , 742 ~ 745 Kämpfer B et al . Z Phys , 1995 , A353 : 71 Z Phys 0572.25, 0572.34 Spported in part by the National Natural Science Foundation of China, and by Shanghai Natural Science Foundation under contract No.97ZA14009 1999-03-30 2000-02-01 2021-02-05 2000 Nuclear Science and Techniques 1 11