Thermal Vorticity Research Articles

Reexamination of local spin polarization beyond global equilibrium in relativistic heavy ion collisions

We study local spin polarization in the relativistic hydrodynamic model. Generalizing the Wigner functions previously obtained from chiral kinetic theory by Y. Hidaka et al. [Phys. Rev. D 97, 016004 (2018)] to the massive case, we present the possible contributions up to the order of $\hbar$ from thermal vorticity, shear viscous tensor, other terms associated with the temperature and chemical-potential gradients, and electromagnetic fields to the local spin polarization. We then implement the (3+1)-dimensional viscous hydrodynamic model to study the spin polarizations from these sources with a small chemical potential and ignorance of electromagnetic fields by adopting an equation of state different from those in other recent studies. Although the shear correction alone upon the local polarization results in a sign and azimuthal-angle dependence more consistent with experimental observations, as also discovered in other recent studies, it is mostly suppressed by the contributions from thermal vorticity and other terms that yield an opposite trend. It is found that the total local spin polarization can be very sensitive to the equation of states, the ratio of shear viscosity to entropy density, and the freeze-out temperature.

Transport Model Approach to Λ and Λ¯ Polarization in Heavy-Ion Collisions

This paper investigates the symmetry breaking between the polarizations of Λ and Λ¯ hyperons in relativistic collisions of heavy ions at intermediate and low energies. The microscopic transport model UrQMD is employed to study the thermal vorticity of hot and dense nuclear matter formed in non-central Au + Au collisions at center-of-mass energies 7.7≤sNN≤62.4 GeV. The whole volume of an expanding fireball is subdivided into small cubic cells. Then, we trace the final Λ and Λ¯ hyperons back to their last interaction point within a certain cell. Extracting the bulk parameters, such as energy density, net baryon density, and net strangeness of the hot and dense medium in the cell, one can obtain the cell temperature and the chemical potentials at the time of the hyperon emission. To do this, the extracted characteristics have to be fitted to the statistical model (SM) of ideal hadron gas. After that, the vorticity of nuclear matter and polarization of both hyperons are calculated. We found that the polarization of both Λ and Λ¯ increases with decreasing energy of heavy-ion collisions. The stronger polarization of Λ¯ is explained by (i) the slightly different freeze-out conditions of both hyperons and (ii) the different space–time distributions of Λ and Λ¯.

Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field

We derive the general exact forms of the Wigner function, of mean values of conserved currents, of the spin density matrix, of the spin polarization vector and of the distribution function of massless particles for the free Dirac field at global thermodynamic equilibrium with rotation and acceleration, extending our previous results obtained for the scalar field. The solutions are obtained by means of an iterative method and analytic continuation, which lead to formal series in thermal vorticity. In order to obtain finite values, we extend to the fermionic case the method of analytic distillation introduced for bosonic series. The obtained mean values of the stress-energy tensor, vector and axial currents for the massless Dirac field are in agreement with known analytic results in the special cases of pure acceleration and pure rotation. By using this approach, we obtain new expressions of the currents for the more general case of combined rotation and acceleration and, in the pure acceleration case, we demonstrate that they must vanish at the Unruh temperature.

Shear-Induced Spin Polarization in Heavy-Ion Collisions.

We study the spin polarization generated by the hydrodynamic gradients. In addition to the widely studied thermal vorticity effects, we identify an undiscovered contribution from the fluid shear. This shear-induced polarization (SIP) can be viewed as the fluid analog of strain-induced polarization observed in elastic and nematic materials. We obtain the explicit expression for SIP using the quantum kinetic equation and linear response theory. Based on a realistic hydrodynamic model, we compute the differential spin polarization along both the beam direction z[over ^] and the out-plane direction y[over ^] in noncentral heavy-ion collisions at sqrt[s_{NN}]=200 GeV, including both SIP and thermal vorticity effects. We find that SIP contribution always shows the same azimuthal angle dependence as experimental data and competes with thermal vorticity effects. In the scenario that Λ inherits and memorizes the spin polarization of a strange quark, SIP wins the competition, and the resulting azimuthal angle dependent spin polarization P_{y} and P_{z} agree qualitatively with the experimental data.

Generating Spin Polarization from Vorticity through Nonlocal Collisions

We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-1/2 particles. To next-to-lowest order in ℏ, it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudogauge, the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes in global equilibrium and that the spin potential is, then, equal to the thermal vorticity. In the nonrelativistic limit, the equations of motion for the energy-momentum and spin tensors reduce to the well-known form for hydrodynamics for micropolar fluids.

Spin-thermal shear coupling in a relativistic fluid

We show that spin polarization of a fermion in a relativistic fluid at local thermodynamic equilibrium can be generated by the symmetric derivative of the four-temperature vector, defined as thermal shear. As a consequence, besides vorticity, acceleration and temperature gradient, also the shear tensor contributes to the polarization of particles in a fluid. This contribution to the spin polarization vector, which is entirely non-dissipative, adds to the well known term proportional to thermal vorticity and may thus have important consequences for the solution of the local polarization puzzles observed in relativistic heavy ion collisions.

Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: scalar field

We derive a general exact form of the phase space distribution function and the thermal expectation values of local operators for the free quantum scalar field at equilibrium with rotation and acceleration in flat space-time without solving field equations in curvilinear coordinates. After factorizing the density operator with group theoretical methods, we obtain the exact form of the phase space distribution function as a formal series in thermal vorticity through an iterative method and we calculate thermal expectation values by means of analytic continuation techniques. We separately discuss the cases of pure rotation and pure acceleration and derive analytic results for the stress-energy tensor of the massless field. The expressions found agree with the exact analytic solutions obtained by solving the field equation in suitable curvilinear coordinates for the two cases at stake and already — or implicitly — known in literature. In order to extract finite values for the pure acceleration case we introduce the concept of analytic distillation of a complex function. For the massless field, the obtained expressions of the currents are polynomials in the acceleration/temperature ratios which vanish at 2π, in full accordance with the Unruh effect.

Relaxation time for the alignment between the spin of a finite-mass quark or antiquark and the thermal vorticity in relativistic heavy-ion collisions

We study the relaxation time required for the alignment between the spin of a finite-mass quark/antiquark and the thermal vorticity, at finite temperature and baryon chemical potential, in the context of relativistic heavy-ion collisions. The relaxation time is computed as the inverse of the total reaction rate that in turn is obtained from the imaginary part of the quark/antiquark self-energy. We model the interaction between spin and thermal vorticity within the medium by means of a vertex coupling quarks and thermal gluons that, for a uniform temperature, is proportional to the global angular velocity and inversely proportional to the temperature. We use realistic estimates for the angular velocities for different collision energies and show that the effect of the quark mass is to reduce the relaxation times as compared to the massless quark case. Using these relaxation times we estimate the intrinsic quark and antiquark polarizations produced by the thermal vorticity. We conclude by pointing out that, in spite of the former being larger than the latter, it is still possible to understand recent results from the STAR Beam Energy Scan when accounting for the fact that only a portion of quarks/antiquarks come from the denser and thus thermalized region in the collision.

Quark spin – thermal vorticity alignment and the polarization in heavy-ion collisions

It has been proposed that the Λ and polarizations observed in heavy-ion collisions are due to the interaction between quark spin and thermal vorticity. In this work we report on a computation of the relaxation time required for this alignment to occur at finite temperature and baryon chemical potential, considering quarks with a finite mass. The calculation is performed after modelling the interaction by means of an effective vertex which couples the thermal gluons and quarks within the vortical medium. We show that the effect of the quark mass is to reduce the relaxation time as compared to the massless quark case. An intrinsic global polarization of quarks/antiquarks emerges which is shown to be linked with the polarization.

Is different Λ and [formula omitted] polarization caused by different spatio-temporal freeze-out picture?

Thermal vorticity in non-central Au+Au collisions at energies 7.7≤s≤62.4 GeV is calculated within the UrQMD transport model. Tracing the Λ and Λ¯ hyperons back to their last interaction point we were able to obtain the temperature and the chemical potentials at the time of emission by fitting the extracted bulk characteristics of hot and dense medium to statistical model of ideal hadron gas. Then the polarization of both hyperons was calculated. The polarization of Λ and Λ¯ increases with decreasing energy of nuclear collisions. The stronger polarization of Λ¯ is explained by the different space-time distributions of Λ and Λ¯ and by different freeze-out conditions of both hyperons.

Fluid dynamics study of the varLambda polarization for Au + Au collisions at sqrt{s_{NN}}=200 GeV

With a Yang–Mills field, stratified shear flow initial state and a high resolution (3+1)D particle-in-cell relativistic (PICR) hydrodynamic model, we calculate the varLambda polarization for peripheral Au + Au collisions at RHIC energy of sqrt{S_{NN}}=200 GeV. The obtained longitudinal polarization in our model agrees with the experimental signature and the quadrupole structure on transverse momentum plane. It is found that the relativistic correction (2nd term), arising from expansion and from the time component of the thermal vorticity, plays a crucial role in our results. This term is changing sign and exceeds the first term, arising from the classical vorticity. Finally, the global polarization in our model shows no significant dependence on rapidity, which agrees with the experimental data. It is also found that the second term flattens the sharp peak arising from the classical vorticity (1st term).

Relaxation time for quark spin and thermal vorticity alignment in heavy-ion collisions

We compute the relaxation time for quark/antiquark spin and thermal vorticity alignment in a quark-gluon plasma at finite temperature and quark chemical potential. We model the interaction of quark/antiquark spin with thermal vorticity as driven by a phenomenological modification of the elementary quark interaction with gluons. We find that in a scenario where the angular velocity of the quark-gluon plasma produced in a peripheral heavy-ion collision is small, quarks/antiquarks take a long time to align their spin with the vorticity. However, when the angular velocity created in the reaction is large, the alignment is efficient and well within the lifetime of the system created in the reaction. The relaxation time is larger for antiquarks which points out to a difference for the polarization of hadrons and antihadrons when this alignment is preserved during hadronization.

Longitudinal spin polarization in a thermal model

We use a thermal model with single freeze-out to determine longitudinal polarization of $\Lambda$ hyperons emitted from a hot and rotating hadronic medium. We consider the top RHIC energies and use the model parameters determined in the previous analyses of particle spectra and elliptic flow. Using a direct connection between the spin polarization tensor and thermal vorticity, we reproduce earlier results which indicate a quadrupole structure of the longitudinal component of the polarization three-vector with an opposite sign compared to that found in the experiment. We further use only the spatial components of the thermal vorticity in the laboratory system to define polarization and show that this leads to the correct sign and magnitude of the quadrupole structure. This procedure resembles a non-relativistic connection between the polarization three-vector and vorticity employed in other works. In general, our results bring further evidence that the spin polarization dynamics in heavy-ion collisions may be not directly related to the thermal vorticity. The additional material explains the construction of the hydrodynamicaly consistent gradients of fluid velocity and temperature in thermal models with the help of the perfect-fluid equations of motion.

Effects of rotation and acceleration in the axial current: density operator vs Wigner function

The hydrodynamic coefficients in the axial current are calculated on the basis of the equilibrium quantum statistical density operator in the third order of perturbation theory in thermal vorticity tensor both for the case of massive and massless fermions. The coefficients obtained describe third-order corrections to the Chiral Vortical Effect and include the contribution from local acceleration. We show that the methods of the Wigner function and the statistical density operator lead to the same result for an axial current in describing effects associated only with vorticity when the local acceleration is zero, but differ in describing mixed effects for which both acceleration and vorticity are significant simultaneously.

Thermal vorticity and thermal chirality in relativistic thermally conducting fluid

The present work focuses on the study of dissipation caused by heat flow in a Carter’s theory of a heat conducting fluid which is expected to be applicable to a particular astrophysical context like early phases of evolution of stellar objects that are far from thermal equilibrium. The dynamical response of entropy fluid in the interaction of heat flow with the motion of matter part of fluid is investigated on the basis of a pair of Maxwell’s like equations that govern the evolution of a heat conducting fluid pioneered by Carter. It is found that the variation of thermal vorticity flux along thermal vorticity tube is coupled to the twist of fluid’s vortex tube and to the spacelike twist of heat flow lines. The proper time rate of change of the thermal vorticity flux in a stream tube associated with the motion of the entropy fluid is related to the combined effect of fluid’s vorticity and spaclike twist of heat flow lines together with the existence of string like structure formed by the entropy flow lines and -lines associated with a particular evolution equation. A covariant solution of a pair of Maxwell’s like equations governing the motion of a heat conducting fluid is obtained under the assumption that the background spacetime representing the gravitational field of a heat conducting fluid is non-circular axisymmetric and stationary. In this case it is shown that the existence of meridional circulation of matter part of fluid is essential for the survival of toroidal components of heat flow vector. A conserved physical quantity called thermal chirality associated with the non-conserved thermal helicity is shown to exist under the assumption that the entropy fluid is in uniform rotation. The relation between the effective thermal angular momentum per entropon of the entropy fluid and twist of heat flow lines is obtained. It is shown that the heat flow causes the twist of the entropy fluid’s vortex lines if the entropy fluid flows are axisymmetric stationary and without meridional circulations but with uniform rotation.

Thermal vorticity and spin polarization in heavy-ion collisions

The hot and dense matter generated in heavy-ion collisions contains intricate vortical structure in which the local fluid vorticity can be very large. Such vorticity can polarize the spin of the produced particles. We study the event-by-event generation of the so-called thermal vorticity in Au + Au collisions at energy region $\sqrt{s}=7.7-200$ GeV and calculate its time evolution, spatial distribution, etc., in a multiphase transport (AMPT) model. We then compute the spin polarization of the $\Lambda$ and $\bar{\Lambda}$ hyperons as a function of $\sqrt{s}$, transverse momentum $p_T$, rapidity, and azimuthal angle. Furthermore, we study the harmonic flow of the spin, in a manner analogous to the harmonic flow of the particle number. The measurement of the spin harmonic flow may provide a way to probe the vortical structure in heavy-ion collisions. We also discuss the spin polarization of $\Xi^0$ and $\Omega^-$ hyperons which may provide further information about the spin polarization mechanism of hadrons.

Polarization in HIC: comparison of methods

Based on the Wigner function for an medium with thermal vorticity, an exact non-perturbative formula for axial current was obtained. It is confirmed that the Chiral Vortical Effect results from the Wigner function. It is shown that the angular velocity and acceleration play the role of new chemical potentials, which is expressed in the appearance of combination $$\mu \pm \,(\Omega \pm i\left| a \right|)/2$$. It is shown that acceleration enters in the form of imaginary chemical potential and the consequences of this fact are investigated. An expression for the boundary temperature for a medium of fermions, which simultaneously has acceleration and rotation, is derived. This temperature in the particular case coincides with the temperature of Unruh.

General thermodynamic equilibrium with axial chemical potential for the free Dirac field

We calculate the constitutive equations of the stress-energy tensor and the currents of the free massless Dirac field at thermodynamic equilibrium with acceleration and rotation and a conserved axial charge by using the density operator approach. We carry out an expansion in thermal vorticity to the second order with finite axial chemical potential μA. The obtained coefficients of the expansion are expressed as correlators of angular momenta and boost operators with the currents. We confirm previous observations that the axial chemical potential induces non-vanishing components of the stress-energy tensor at first order in thermal vorticity due to breaking of parity invariance of the density operator with μA ≠ 0. The appearance of these components might play an important role in chiral hydrodynamics.

Magneto-vortical evolution of QGP in heavy ion collisions

The interplay of magnetic field and thermal vorticity in a relativistic ideal fluid might generate fluid vorticity during the fluid evolution provided the flow fields and the entropy density of the fluid is inhomogeneous (Mahajan and Yoshida 2010 Phys. Rev. Lett. 105, 095005). Exploiting this fact and assuming a large magnetic Reynolds number we study the evolution of a generalized magnetic field () which is defined as a combination of the usual magnetic field () and relativistic thermal vorticity (ωμν), in a 2(space) + 1(time) dimensional isentropic evolution of quark–gluon plasma with longitudinal boost invariance. The temporal evolution of is found to be different than , and the evolution also depends on the position of the fluid along the beam direction (taken along the z axis) with respect to the mid-plane z = 0. Further it is observed that the transverse components () evolve differently around the mid-plane.

The Quasi-Biweekly Oscillation of Winter Precipitation Associated with ENSO over Southern China

Using ERA-interim Reanalysis data and observational data, the intraseasonal oscillation of the winter rainfall in southern China is studied. The mean square deviation of daily precipitation is used to express precipitation variability, and winter precipitation variability over southern China is determined to be highly correlated with sea surface temperature (SST) in central and eastern tropical Pacific; the dominant period of the precipitation is 10–30 days, which reflects quasi-biweekly oscillation. Examination of 1000 hPa geopotential height suggests that key low-pressure systems affecting the intraseasonal precipitation come from Lake Baikal, but with different travel paths. In El Niño years, key low-pressure systems converge with other low-pressure systems and move southeastward until reaching South China, while in La Niña years, only one low-pressure system can reach southern China. Meanwhile, the explosive development of the low-pressure system is mainly caused by the joint effects of thermal advection and vorticity advection in El Niño, and only vorticity advection accounted for the dominant status in La Niña. Multiscale analysis shows that the meridional distribution of intraseasonal circulation plays an important role on the thermal transmission and brings strong warm advection from low latitudes to high latitudes in El Niño.