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bstract
Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED ...and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient: the rotational viscosity. We study linear response theory and observe an interesting mode mixing phenomenon between the transverse shear and the spin density modes. We propose several field-theoretical ways to compute the spin relaxation time and the rotational viscosity, via the Green-Kubo formula based on retarded correlation functions.
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bstract
We study the anomaly induced effects of dense baryonic matter under rotation. We derive the anomalous terms that account for the chiral vortical effect in the low-energy effective theory ...for light Nambu-Goldstone modes. The anomalous terms lead to new physical consequences, such as the anomalous Hall energy current and spontaneous generation of angular momentum in a magnetic field (or spontaneous magnetization by rotation). In particular, we show that, due to the presence of such anomalous terms, the ground state of the quantum chromodynamics (QCD) under sufficiently fast rotation becomes the “chiral soliton lattice” of neutral pions that has lower energy than the QCD vacuum and nuclear matter. We briefly discuss the possible realization of the chiral soliton lattice induced by a fast rotation in noncentral heavy ion collisions.
We give a theoretical perspective on the vorticity and spin polarization in heavy-ion collisions. We discuss the recent progress in spin hydrodynamics and spin kinetic theory. We also discuss other ...effects caused by vorticity including the chiral vortical effect and rotation-induced phase transitions.
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bstract
The spin Hall effect of light attracted enormous attention in the literature due to the ongoing progress in developing of new optically active materials and metamaterials with non-trivial ...spin-orbit interaction. Recently, it was shown that rotating fermionic systems with relativistic massless spectrum may exhibit a 3-dimensional analogue of the spin Hall current — the chiral vortical effect (CVE). Here we show that CVE is a general feature of massless particles with an arbitrary spin. We derive the semi-classical equations of motion in rotating frame from the first principles and show how by coordinate transformation in the phase space it can be brought to the intuitive form proposed in
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. Our finding clarifies the superficial discrepancies in different formulations of the chiral kinetic theory for rotating systems. We then generalize the chiral kinetic theory, originally introduced for fermions, to an arbitrary spin and study chirality current in a general rotating chiral medium. We stress that the higher-spin realizations of CVE can be in principle observed in various setups including table-top experiments on quantum optics.
We derive relativistic hydrodynamic equations with a dynamical spin degree of freedom on the basis of an entropy-current analysis. The first and second laws of local thermodynamics constrain possible ...structures of the constitutive relations including a spin current and the antisymmetric part of the (canonical) energy-momentum tensor. Solving the obtained hydrodynamic equations within the linear-mode analysis, we find spin-diffusion modes, indicating that spin density is damped out after a characteristic time scale controlled by transport coefficients introduced in the antisymmetric part of the energy-momentum tensor in the entropy-current analysis. This is a consequence of mutual convertibility between spin and orbital angular momentum.
We study a relativistic plasma containing charged chiral fermions in an external electric field. We show that with the presence of both vector and axial charge densities, the electric field can ...induce an axial current along its direction and thus cause chirality separation. We call it the chiral electric separation effect (CESE). On a very general basis, we argue that the strength of CESE is proportional to μ(V)μ(A) with μ(V) and μ(A) the chemical potentials for vector charge and axial charge. We then explicitly calculate this CESE conductivity coefficient in thermal QED at leading-log order. The CESE can manifest a new gapless wave mode propagating along the electric field. Potential observable effects of CESE in heavy-ion collisions are also discussed.
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