13–16 Jan 2025
Asia/Kolkata timezone

On the convergence of the gradient expansion of the Boltzmann equation

15 Jan 2025, 16:11
7m
2. Initial State - pre-equilibrium dynamics, baryon stopping, intense electromagnetic field Parallel A

Speaker

Reghukrishnan Gangadharan

Description

When two heavy nuclei collide in relativistic heavy ion collisions, the resulting
system is initially in a non-equilibrium state. The evolution of the system
towards equilibrium can be studied by using the Boltzmann equation.
However, approximating the solution to the Boltzmann equation using a
gradient expansion leads to a divergent series. Using an integral solution to
the Boltzmann equation in relaxation time approximation, we obtain its full
gradient expansion which contains exponentially decaying non-hydrodynamic
terms. It is shown that this gradient expansion can have a finite radius of
convergence. We further argue that, in the relaxation time model, proximity
to local thermal equilibrium is not necessary for the system to be described by
hydrodynamic equations.

Author

Presentation materials