Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow

被引:56
|
作者
Jaiswal, Sunil [1 ]
Chattopadhyay, Chandrodoy [2 ]
Jaiswal, Amaresh [3 ]
Pal, Subrata [1 ]
Heinz, Ulrich [2 ,4 ]
机构
[1] Tata Inst Fundamental Res, Dept Nucl & Atom Phys, Mumbai 400005, Maharashtra, India
[2] Ohio State Univ, Dept Phys, 174 W 18th Ave, Columbus, OH 43210 USA
[3] HBNI, Natl Inst Sci Educ & Res, Sch Phys Sci, Jatni 752050, Odisha, India
[4] Goethe Univ Frankfurt, Inst Theoret Phys, Max von Laue Str 1, D-60438 Frankfurt, Germany
基金
美国国家科学基金会;
关键词
QUARK-GLUON PLASMA; NUCLEUS COLLISIONS; THERMODYNAMICS; HYDRODYNAMICS; VISCOSITY; STABILITY;
D O I
10.1103/PhysRevC.100.034901
中图分类号
O57 [原子核物理学、高能物理学];
学科分类号
070202 ;
摘要
We consider causal higher order theories of relativistic viscous hydrodynamics in the limit of one-dimensional boost-invariant expansion and study the associated dynamical attractor. We obtain evolution equations for the inverse Reynolds number as a function of Knudsen number. The solutions of these equations exhibit attractor behavior which we analyze in terms of Lyapunov exponents using several different techniques. We compare the attractors of the second-order Mfiller-Israel-Stewart (MIS), transient Denicol-Niemi-Molnar-Rischke (DNMR), and third-order theories with the exact solution of the Boltzmann equation in the relaxation-time approximation. It is shown that for Bjorken flow the third-order theory provides a better approximation to the exact kinetic theory attractor than both MIS and DNMR theories. For three different choices of the time dependence of the shear relaxation rate we find analytical solutions for the energy density and shear stress and use these to study the attractors analytically. By studying these analytical solutions at both small and large Knudsen numbers we characterize and uniquely determine the attractors and Lyapunov exponents. While for small Knudsen numbers the approach to the attractor is exponential, strong power-law decay of deviations from the attractor and rapid loss of initial state memory are found even for large Knudsen numbers. Implications for the applicability of hydrodynamics in far-off-equilibrium situations are discussed.
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页数:15
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