Second-order relativistic hydrodynamics is surprisingly predictive, even in the presence of large gradients. The hydrodynamic expansion from the method of moments does not require a gradient expansion, but it is intrinsically bound to the classic nature of relativistic kinetic theory. In this work a modified version of the method of moments is applied the Wigner distribution (the quantum precursor of the distribution function) to recover a systematically improvable hydrodynamic expansion, avoiding the divergences that would otherwise appear in the quantum case. The convergence of the regularized expansion is checked numerically in a far from equilibrium, distant from the kinetic limit case.
Newly introduced equilibrium Wigner functions for particles with spin one-half are used in the semi-classical kinetic equations to study a possible relation between thermal vorticity and spin polarization. It is shown that in global equilibrium both the thermal-vorticity and spin polarization tensors are constant but not necessarily equal. In the case of local equilibrium, we define a procedure leading to hydrodynamic equations with spin. We introduce such equations for the de~Groot, van~Leeuwen, and van~Weert (GLW) formalism as well as for the canonical scheme (these two frameworks differ by …
The evolution equation for the energy-momentum moments of the non-equilibrium density function & The regularized relativistic third order hydrodynamics
The formulation of relativistic hydrodynamics for massive particles with spin 1/2 is shortly reviewed. The proposed framework is based on the Wigner function treated in a semi-classical approximation or, alternatively, on a classical treatment of spin 1/2. Several theoretical issues regarding the choice of the energy-momentum and spin tensors used to construct the hydrodynamic framework with spin are discussed in parallel.
Recently introduced equilibrium Wigner functions for spin-one-half particles are used in the semiclassical kinetic equations to study the relation between spin polarization and vorticity. It is found, in particular, that such a framework does not necessarily imply that the thermal-vorticity and spin polarization tensors are equal. Subsequently, a procedure to formulate the hydrodynamic framework for particles with spin-one-half, based on the semiclassical expansion, is outlined.
We present a general systematic formalism for describing dynamics of fluctuations in an arbitrary relativistic hydrodynamic flow, including their feedback (known as long-time hydrodynamic tails). The fluctuations are described by two-point equal-time correlation functions. We introduce a definition of equal time in a situation where the local rest frame is determined by the local flow velocity, and a method of taking derivatives and Wigner transforms of such equal-time correlation functions, which we call confluent. We find that the equations for confluent Wigner functions not only resemble ki…
We present the explicit expressions of different pseudo-gauge transformations for Dirac and Proca fields considering a general interaction term. The particular case of the interaction of Dirac and Proca fields with a background electromagnetic field is also studied. Starting from the quantum kinetic theory with collisions derived from the Wigner-function formalism for massive spin-1/2 and spin-1 particles, we establish a connection between different pseudo-gauges and relativistic spin hydrodynamics. The physical implications of the various decompositions of orbital and spin angular momentum ar…
We study the Wigner function for massive spin-1/2 fermions in electromagnetic fields. Dirac form kinetic equation and Klein-Gordon form kinetic equation are obtained for the Wigner function, which are derived from the Dirac equation. The Wigner function and its kinetic equations are expanded in terms of the generators of Clifford algebra and a complicated system of partial differential equations is obtained. We prove that some component equations are automattically satisfied if the rest ones are fulfilled. In this thesis two methods are proposed for calculating the Wigner function, which are p…
We systematically analyze the effects of the derivatives of the hydrodynamic fields on axial Wigner function that describes the spin polarization vector in phase space. We have included all possible first-order derivative contributions that are allowed by symmetry and compute the associated transport functions at one-loop using the linear response theory. In addition to reproducing known effects due to the temperature gradient and vorticity, we have identified a number of potentially significant contributions that are overlooked previously. In particular, we find that the shear strength, the s…
Recent progress in the formulation of relativistic hydrodynamics for particles with spin one-half is reviewed. We start with general arguments advising introduction of a tensor spin chemical potential that plays a role of the Lagrange multiplier coupled to the spin angular momentum. Then, we turn to a discussion of spin-dependent distribution functions that have been recently proposed to construct a hydrodynamic framework including spin and serve as a tool in phenomenological studies of hadron polarization. Distribution functions of this type are subsequently used to construct the equilibrium …
We introduce the quantum-field-theory (QFT) derivation of chiral kinetic theory (CKT) from the Wigner-function approach, which manifests side jumps and non-scalar distribution functions associated with Lorentz covariance and incorporates both background fields and collisions. The formalism is utilized to investigate second-order responses of chiral fluids near local equilibrium. Such non-equilibrium anomalous transport is dissipative and affected by interactions. Contributions from both quantum corrections in anomalous hydrodynamic equations (EOM) of motion and those from the CKT and Wigner fu…
Despite the fact that a system created in relativistic heavy ion collisions is an isolated quantum system, which cannot increase its entropy in the course of unitary quantum evolution, hydrodynamical analysis of experimental data seems to indicate that the matter formed in the collisions is thermalized very quickly. Based on common consideration of hydrodynamics as an effective theory in the domain of slow- and long-length modes, we discuss the physical mechanisms responsible for the decoherence and emergence of the hydrodynamic behavior in such collisions, and demonstrate how such physical me…
We study the kinetic theory for a (2+1)-dimensional fermionic system with special emphasis on the parity violating properties associated with the fermion mass. The Wigner function approach is used to derive hydrodynamical transport coefficients to the first spatial derivative order. As a first attempt, the collisions between fermions are neglected. The resulting system is dissipationless. The parity violating Hall electric conductivity has the same temperature and chemical potential dependence as the quantum field theory result at one-loop. Vorticity dependent transport properties, which were …
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…
A modified quantum kinetic equation which takes account of the noninertial features of rotating frame is proposed. The vector and axial-vector field components of the Wigner function for chiral fluids are worked out in a semiclassical scheme. It is demonstrated that the chiral currents and energy-momentum tensor computed by means of them are consistent with the hydrodynamical results. A new semiclassical covariant chiral transport equation is established by inspecting the equations satisfied by the chiral vector fields. It uniquely provides a new three-dimensional semiclassical chiral kinetic …
The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be non-trivially introduced in a co-moving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (…
