We derive the nonequilibrium kinetic equation describing the motion of chiral massless particles in the regime where it can be considered classically. We show that the Berry monopole which appears at the origin of the momentum space due to level crossing is responsible for the chiral magnetic and vortical effects.

We show that Lorentz invariance is realized nontrivially in the classical action of a massless spin-1 2 particle with definite helicity. We find that the ordinary Lorentz transformation is modified by a shift orthogonal to the boost vector and the particle momentum. The shift ensures angular momentum conservation in particle collisions and implies a nonlocality of the collision term in the Lorentz-invariant kinetic theory due to side jumps. We show that 2/3 of the chiral-vortical effect for a uniformly rotating particle distribution can be attributed to the magnetic moment coupling required by the Lorentz invariance. We also show how the classical action can be obtained by taking the classical limit of the path integral for a Weyl particle.

The search for the QCD critical point in heavy-ion collision experiments requires dynamical simulations of the bulk evolution of QCD matter as well as of fluctuations. We consider two essential ingredients of such a simulation: a generic extension of hydrodynamics by a parametrically slow mode or modes ("Hydroþ") and a description of fluctuations out of equilibrium. By combining the two ingredients, we are able to describe the bulk evolution and the fluctuations within the same framework. Critical slowing-down means that equilibration of fluctuations could be as slow as hydrodynamic evolution, and thus fluctuations could significantly deviate from equilibrium near the critical point. We generalize hydrodynamics to partial-equilibrium conditions where the state of the system is characterized by the off-equilibrium magnitude of fluctuations in addition to the usual hydrodynamic variables-conserved densities. We find that the key element of the new formalism-the extended entropy taking into account the off-equilibrium fluctuations-is remarkably similar to the 2PI action in the quantum field theory. We show how the new Hydroþ formalism reproduces two major effects of critical fluctuations on the bulk evolution: the strong frequency dependence of the anomalously large bulk viscosity as well as the stiffening of the equation of state with an increasing frequency or wave number. While the agreement with known results confirms its validity, the fact that Hydroþ achieves this within a local and deterministic framework gives it significant advantages for dynamical simulations.

We derive a coupled set of equations that describe the non-equilibrium evolution of cumulants of critical fluctuations for space-time trajectories on the cross-over side of the QCD phase diagram. In particular, novel expressions are obtained for the non-equilibrium evolution of non-Gaussian Skewness and Kurtosis cumulants. Utilizing a simple model of the space-time evolution of a heavyion collision, we demonstrate that, depending on the relaxation rate of critical fluctuations, Skewness and Kurtosis can differ significantly in magnitude as well as in sign from equilibrium expectations. Memory effects are important and shown to persist even for trajectories that skirt the edge of the critical regime. We use phenomenologically motivated parameterizations of freeze-out curves, and of the beam energy dependence of the net baryon chemical potential, to explore the implications of our model study for the critical point search in heavy-ion collisions.

We compute the momentum diffusion coefficients of heavy quarks, κ and κ ⊥ , in a strong magnetic field B along the directions parallel and perpendicular to B, respectively, at the leading order in QCD coupling constant α s . We consider a regime relevant for the relativistic heavy ion collisions, α s eB T 2 eB, so that thermal excitations of light quarks are restricted to the lowest Landau level (LLL) states. In the vanishing light-quark mass limit, we find κ LO ⊥ ∝ α 2 s T eB in the leading order that arises from screened Coulomb scatterings with (1+1)-dimensional LLL quarks, while κ gets no contribution from the scatterings with LLL quarks due to kinematic restrictions. We show that the first non-zero leading order contributions to κ LO come from the two separate effects: 1) the screened Coulomb scatterings with thermal gluons, and 2) a finite light-quark mass m q . The former leads to κ LO, gluon ∝ α 2 s T 3 and the latter to κ LO, massive ∝ α s (α s eB) 1/2 m 2 q . Based on our results, we propose a new scenario for the large value of heavy-quark elliptic flow observed in RHIC and LHC. Namely, when κ ⊥ κ , an anisotropy in drag forces gives rise to a sizable amount of the heavy-quark elliptic flow even if heavy quarks do not fully belong to an ellipsoidally expanding background fluid. *