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arXiv 1602.00573nucl-thhep-phphysics.flu-dyn
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从Boltzmann方程导出各向异性耗散流体动力学

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

E. Molnar, H. Niemi, D. H. Rischke

备注：
52 pages; Abstract slightly changed; new references and new paragraph added
发表信息：
Phys. Rev. D 93, 114025 (2016)
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摘要：

流体动力学运动方程可以从玻尔兹曼方程中导出，其围绕处于局部热力学平衡的单粒子分布函数展开，即，在流体元素的静止坐标系中的动量空间中各向同性。然而，在单粒子分布函数在动量空间中是高度各向异性的情况下，例如相对论能量下重离子碰撞的初始阶段，这种扩展必然会破裂。尽管如此，人们仍然可以推导出一种流体动力学理论，称为各向异性耗散流体动力学，根据围绕单粒子分布函数$\hat{f}_{0\bf k}$的展开，它通过适当的参数化包含（至少部分）动量各向异性。我们构造这样的展开在能量和动量的各向异性的方向和不可约张量的二维动量子空间正交的流体速度和各向异性的方向的多项式。从玻尔兹曼方程，我们然后推导出一组运动方程的不可约的时刻的偏差的单粒子分布函数从$\hat{f}_{0\bf k}$。通过14阶矩近似截断这一组，我们得到各向异性耗散流体动力学的运动方程。

英文摘要：

Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, called anisotropic dissipative fluid dynamics, in terms of an expansion around a single-particle distribution function, $\hat{f}_{0\bf k}$, which incorporates (at least parts of) the momentum anisotropy via a suitable parametrization. We construct such an expansion in terms of polynomials in energy and momentum in the direction of the anisotropy and of irreducible tensors in the two-dimensional momentum subspace orthogonal to both the fluid velocity and the direction of the anisotropy. From the Boltzmann equation we then derive the set of equations of motion for the irreducible moments of the deviation of the single-particle distribution function from $\hat{f}_{0\bf k}$. Truncating this set via the 14-moment approximation, we obtain the equations of motion of anisotropic dissipative fluid dynamics.

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