Causal hydrodynamics from kinetic theory by doublet scheme in renormalization-group method

Understand

We develop a general framework in the renormalization-group (RG) method for extracting a mesoscopic dynamics from an evolution equation by incorporating some excited (fast) modes as additional components to the invariant manifold spanned by zero modes.

• We call this framework the doublet scheme.
• The validity of the doublet scheme is first tested and demonstrated by taking the Lorenz model as a simple three-dimensional dynamical system; it is shown that the two-dimensional reduced dynamics on the attractive manifold composed of the would-be zero and a fast modes are successfully obtained in a natural way.
• We then apply the doublet scheme to construct causal hydrodynamics as a mesoscopic dynamics of kinetic theory, i.e., the Boltzmann equation, in a systematic manner with no ad-hoc assumption.