Mathematical analysis

Psychology

Kinetic theory

Social psychology

Kinetic energy

Gauge theory

Transient (computer programming)

Physics

Mathematics

Mathematical physics

RADIUS

Theoretical physics

Quantum mechanics

Operating system

Analytic continuation

Radius of convergence

Relaxation (psychology)

Computer science

Power series

Statistical physics

Gravitational singularity

Conformal map

Classical mechanics

Computer security

Physical review. D/Physical review. D.

We explore the transition to hydrodynamics in a weakly-coupled model of quark-gluon plasma given by kinetic theory in the relaxation time approximation with conformal symmetry. We demonstrate that the gradient expansion in this model has a vanishing radius of convergence due to the presence of a transient (nonhydrodynamic) mode, in a way similar to results obtained earlier in strongly-coupled gauge theories. This suggests that the mechanism by which hydrodynamic behaviour emerges is the same, which we further corroborate by a novel comparison between solutions of different weakly and strongly coupled models. However, in contrast with other known cases, we find that not all the singularities of the analytic continuation of the Borel transform of the gradient expansion correspond to transient excitations of the microscopic system: some of them reflect analytic properties of the kinetic equation when the proper time is continued to complex values.

Hydrodynamization in kinetic theory: Transient modes and the gradient expansion