Exact solution of the ( 0+1 )-dimensional Boltzmann equation for a massive gas

Abstract

We solve the one-dimensional boost-invariant kinetic equation for a relativistic massive system with the collision term treated in the relaxation time approximation. The result is an exact integral equation which can be solved numerically by the method of iteration to arbitrary precision. We compare predictions for the shear and bulk viscosities of a massive system with those obtained from the exact solution. Finally, we compare the time evolution of the bulk pressure obtained from our exact solution with results obtained from the dynamical equations of second-order viscous hydrodynamics.

Photon production from a nonequilibrium quark-gluon plasma

“…The four-vector z µ is orthogonal to u µ and in the LRF points in the longitudinal direction (identified with the direction of the dynamicallyevolving anisotropy in the system,n) [40]. 6 This assumption has been tested elsewhere by comparing the predictions of anisotropic hydrodynamics to exact solutions of the Boltzmann equation in a variety of special cases [42][43][44][45][46][47][48][49]. 7 We assume vanishing chemical potential gradients.…”

Anisotropic hydrodynamics for a mixture of quark and gluon fluids

“…One way to achieve this task is to compare the results of various hydrodynamic approaches [2][3][4][5][6][7][8][9][10][11][12], which differ by the number of terms included in the formalism and by the values of the transport coefficients, with the results of the underlying microscopic kinetic theory [13][14][15][16][17][18]. The latter is very often used as a staring point to derive the specific form of the evolution equations of relativistic hydrodynamics, however, several approximations done in such procedures may result in differences between the predictions of the kinetic theory and the hydrodynamic models constructed directly with its help.…”

Applications of dissipative and anisotropic hydrodynamics in description of early stages of relativistic heavy-ion collisions

“…The methods of solving Eq. (1) has been expained in more detail in [17][18][19]. If the solution of the kinetic equation is found, one can calculate the bulk viscous pressure from the equation…”

“…We connect these problems with an incomplete character of various computational schemes which are used to derive the viscous hydrodynamic equations. Our critical examination of the hydrodynamic approaches is based on the comparisons of the hydrodynamic results with the predictions of the underlying kinetic theory [17][18][19].…”