Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1811.04409

Relativistic hydrodynamics for spin-polarized fluids

Wojciech Florkowski·Radoslaw Ryblewski·Avdhesh Kumar
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 Wigner functions that are employed in the semi-classical kinetic equation. The semi-classical expansion elucidates several aspects of the hydrodynamic approach, in particular, shows the ways in which different possible versions of hydrodynamics with spin can be connected by pseudo-gauge transformations. These results point out at using the de~Groot - van~Leeuwen - van~Weert versions of the energy-momentum and spin tensors as the most natural and complete physical variables. Finally, a totally new method is proposed to design hydrodynamics with spin, which is based on the classical treatment of spin degrees of freedom. Interestingly, for small values of the spin chemical potential the new scheme brings the results that coincide with those obtained before. The classical approach also helps us to resolve problems connected with the normalization of the spin polarization three-vector. In addition, it clarifies the role of the Pauli-Lubanski vector and the entropy current conservation. We close our review with several general comments presenting possible future developments of the discussed frameworks.

Explore related subjects

nucl-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Wojciech Florkowski, Radoslaw Ryblewski, Avdhesh Kumar. 2019-07-11. Relativistic hydrodynamics for spin-polarized fluids. https://doi.org/10.1016/j.ppnp.2019.07.001

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Dimer Effective Field Theory

While chiral perturbation theory for mesons is characterized by a momentum expansion in $Q/Λ_χ$ with $Λ_χ\sim 1$ GeV, existing formulations of effective theory for nucleon-nucleon scattering deviate from data at $Q\sim 300$ MeV or lower. We offer heuristic evidence that unsuspected nonanalytic structure exists in the complex momentum plane obstructing the effective field theory expansion in the spin-triplet channels, associated with the peak of the angular momentum barrier whose energy in low partial waves satisfies $k=\sqrt{ME} \sim 300$ MeV. With this motivation, we construct a meromorphic function of $k^2$ we call the $C$-matrix, for which the radius of convergence of its Taylor expansion in $k^2$ is equivalent to that of the momentum expansion of the effective field theory. Thus the range of validity of the effective theory is directly related to the pole structure of the $C$-matrix. We uncover that pole structure and confirm that it is the source of the obstruction. The systematic inclusion of dimer fields as propagating degrees of freedom in the effective theory to account for those poles results in cut-off insensitive fits at order $Q^0$ to most of the lower partial wave phase shifts up to the pion production threshold, using only the one pion exchange part of the long-range nucleon-nucleon interaction. Our theory should be applicable to the singular potentials regularly found in atomic physics as well.

nucl-th↗
arXiv2026

Three-dimensional orbital-free density functional theory description of nuclear pasta in the inner crust of neutron stars

Background: In the bottom layer of the inner crust of neutron stars, various crystalline structures are expected to emerge that are collectively called ``nuclear pasta.'' It is desirable to know properties of nuclear pasta in a wide variety of conditions for astrophysical applications. However, three-dimensional fully-microscopic calculations require huge computational effort that makes it still challenging to carry out systematic calculations. Purpose: In this paper, we propose an efficient method to calculate various nuclear pasta configurations in a non-empirical manner, based on three-dimensional orbital-free density functional theory (OF-DFT). We demonstrate the feasibility of the proposed approach by applying it to densities across the inner crust of neutron stars. Methods: As a first application of OF-DFT for nuclear pasta, we employ the second-order extended Thomas-Fermi (ETF) expansion of Skyrme energy density functional (EDF) to construct an EDF that depends only on neutron and proton number densities. Based on the variational principle, we derive Euler-Lagrange equations to determine optimal neutron and proton density distributions and solve them self-consistently. In this work, we call this approach the self-consistent ETF (SC-ETF) method. Results: We perform three-dimensional SC-ETF calculations with various box sizes. We successfully obtain various pasta structures, depending on given average nucleon number densities, consistent with earlier studies. Moreover, we find other exotic structures, such as bending and/or connected rods, slabs with a hole, etc., underlining the advantage of the self-consistent formalism. Conclusions: We demonstrate that the SC-ETF method proposed in this study, which can be regarded as a realization of OF-DFT, is a promising tool that can efficiently describe complex pasta structures without empirical assumptions on geometric shapes.

nucl-th↗
arXiv2026

Microscopic analysis of M1 scissors mode in $^{254}$No

The low-energy $M1$ orbital scissors mode (SM) was recently observed by Oslo group in deformed nucleus $^{254}$No. This is the heaviest nucleus where SM was ever experimentally found. We propose the analysis of SM, together with the spin-flip $M1$ resonance, within fully self-consistent Quasiparticle Random-Phase Approximation (QRPA) with Skyrme forces SG2, SLy4 and SLy5. The impact of "tensor" $J^2$-term, introduced by perturbative (on the base of SG2) and consistent (SLy5) ways, is analyzed and shown to be noticeable but not decisive. The deformation-induced coupling of $M1$ and $E2$ states is inspected. The calculations reasonably describe Oslo's experimental data. The best agreement is obtained for SLy5. A fine structure of SM in $^{254}$No is predicted. A significant constructive interference of the dominant orbital and minor spin-flip contributions to $M1$ strength at SM energy region is found. What is remarkable, our analysis of distributions of the convective nuclear currents challenges the scissors-like flow usually assumed for SM.

nucl-th↗