Dynamics near QCD critical point by dynamic renormalization group

We work out the basic analysis of dynamics near QCD critical point (CP) by dynamic renormalization group (RG). In addition to the RG analysis by coarse graining, we construct the nonlinear Langevin equation as a basic equation for the critical dynamics. Our construction is based on the generalized Langevin theory and the relativistic hydrodynamics. Applying the dynamic RG to the constructed equation, we derive the RG equation for the transport coefficients and analyze their critical behaviors. We find that the resulting RG equation turns out to be the same as that for the liquid-gas CP except for an insignificant constant. Therefore, the bulk viscosity and the thermal conductivity strongly diverge at the QCD CP. We also show that the thermal and viscous diffusion modes exhibit critical slowing down with the dynamic critical exponents $z_{\rm thermal}\sim 3$ and $z_{\rm viscous}\sim 2$, respectively. In contrast, the sound propagating mode shows critical speeding up with the negative exponent $z_{\rm sound}\sim -0.8$.Comment: 16 pages, 4 figures. accepted version by PRD. A comment on a frame dependence is added in Sec.

Origin of long-range order in a two-dimensional nonequilibrium system under laminar flows

We study long-range order in two dimensions where an order parameter is advected by linear laminar flows. The linear laminar flows include three classes: rotational, shear, and elongational flows. Under these flows, we analyze an ordered state of the $O(N)$ scalar model in the large-$N$ limit. We show that the stability of the ordered state depends on the flow pattern; the shear and elongational flows stabilize but the rotational flow does not. We discuss a physical interpretation of our results based on interaction representation in quantum mechanics. The origin of the long-range order is interpreted from the advection of wavenumbers along the streamlines and its stretching effect stabilizes the order.Comment: 6+5pages, 3+1figure