Derivation of the nonlocal collision term in the relativistic Boltzmann equation for massive spin-1/2 particles from quantum field theory

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

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 dy…

Lorentz-covariant nonlocal collision term for spin-1/2 particles

We revisit the derivation of the nonlocal collision term in the Boltzmann equation for spin-1/2 particles, using both the Wigner-function approach by de Groot, van Leeuwen, and van Weert, and the Kadanoff-Baym equation in $T$-matrix approximation. Contrary to previous calculations, our results maintain full Lorentz covariance of the nonlocal collision term.

Generating spin polarization from vorticity through nonlocal collisions

We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-1/2 particles. To next-to-lowest order in $\hbar$ it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudo-gauge the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes only in global equilibrium and that the spin potential is then equal to the thermal vorticity. In the nonrelativistic limit, the equat…

Relativistic hydrodynamics from Boltzmann equation with modified collision term

Generalizing the collision term in the relativistic Boltzmann equation to include nonlocal effects, and using Grad's 14-moment approximation for the single-particle distribution function, we derive evolution equations for the relativistic dissipative fluid dynamics and compare them with the corresponding equations obtained in the standard Israel-Stewart and related approaches. Significance of this generalization on hydrodynamic evolution is demonstrated in the framework of one-dimensional scaling expansion.

Derivation of second-order relativistic hydrodynamics for reactive multi-component systems

We derive the second-order hydrodynamic equation for reactive multi-component systems from the relativistic Boltzmann equation. In the reactive system, particles can change their species under the restriction of the imposed conservation laws during the collision process. Our derivation is based on the renormalization group (RG) method, in which the Boltzmann equation is solved in an organized perturbation method as faithfully as possible and possible secular terms are resummed away by a suitable setting of the initial value of the distribution function. The microscopic formulae of the relaxati…

高温下共振费米子输运系数的 Boltzmann 方程微观推导

Microscopic derivation of the Boltzmann equation for transport coefficients of resonating fermions at high temperature

本文从 Kubo 公式出发，通过恢复夹点奇异性导致的同阶高阶逸度贡献，微观推导出线性化 Boltzmann 方程，并计算了任意散射长度下共振费米子的剪切黏度与热导率。

Derivation of fluid dynamics from kinetic theory with the 14--moment approximation

We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely man…

Fluctuations due to the nonlocal character of collisions

It is shown that the collision integral describing the nonlocal character of collisions leads to the same mean-field fluctuations as proposed by Boltzmann-Langevin pictures. It is argued that this appropriate collision integral contains the fluctuation-dissipation theorems in equilibrium itself and therefore there is no need to assume additionally stochasticity. This leads to tremendous simplifications in numerical simulation schemes.

Derivation of Covariant Dissipative Fluid Dynamics in the Renormalization-group Method

We derive generic relativistic hydrodynamical equations with dissipative effects from the underlying Boltzmann equation in a mechanical and systematic way on the basis of so called the renormalization-group (RG) method. A macroscopic frame vector is introduced to specify the frame on which the macroscopic dynamics is described. Our method is so mechanical with only few ansatz that our method give a microscopic foundation of the available hydrodynamical equations, and also can be applied to make a reduction of the kinetic equations other than the simple Boltzmann equation.

Simulation of Heavy Ion Reactions with Nonlocal Kinetic Equations

The incorporation of realistic trajectories of two-particle scattering into existing BUU or QMD codes meets considerable difficulties. We propose a method of replacing the scattering event by a tractable non-local scenario reproducing the correct asymptotics. The first principle derivation justifies the use of corresponding nonlocal kinetic equations. The nonlocal shifts are necessary if the system should approach an equation of state with second quantum virial coefficient. The modifications of QMD and BUU codes are discussed and comparison are presented with resent data. We find a pre-equilib…