Speaker
Prof.
Georg Wolschin
(U Heidelberg)
Description
It is proposed to model the local kinetic equilibration in finite systems of
fermions and bosons based on a nonlinear diffusion equation [1,2].
It properly accounts for their quantum-statistical characteristics, and is
solved exactly. The solution is suited to replace the linear relaxation
ansatz that has often been used in the literature.
The microscopic transport coefficients are determined through
the macroscopic variables temperature and local equilibration time.
The model can be applied to high energies typical for relativistic particle
collisions, and to low energies appropriate for cold quantum gases.
With initial conditions that are appropriate for quarks [1] and gluons [2]
in a relativistic heavy-ion collision such as Au-Au or Pb-Pb at energies
reached at RHIC or LHC, the analytical solution is derived. It agrees with
the numerical solution of the nonlinear equation. The analytical expression
for the gluonic local equilibration time in the thermal tail is compared to the
corresponding case for fermions, where Pauli’s principle delays
the thermalisation.
Due to the nonlinearity of the basic equation, sharp edges of the
initial distributions are continously smeared out and local equilibrium with
a thermal tail in the ultraviolett region is rapidly attained [2].
[1] G. Wolschin, Phys. Rev. Lett. 48, 1004 (1982); T. Bartsch, G. Wolschin,
Annals Phys., in press, and arXiv:1806.04044 (2018).
[2] G. Wolschin, Physica A 499,1 (2018); Europhys. Lett. 123, 20009 (2018).
Summary
It is proposed to model the local kinetic equilibration in finite systems of
fermions and bosons based on a nonlinear diffusion equation, which properly accounts
for their quantum-statistical characteristics. In particular, it has the proper
Fermi-Dirac and Bose-Einstein equilibrium limits, and is solved exactly. The solution
is suited to replace the linear relaxation ansatz that has often been used in the literature.
Primary author
Prof.
Georg Wolschin
(U Heidelberg)
