arXiv subjects

Wojciech Florkowski

Publications and source records attributed to Wojciech Florkowski.

At least 19 recordsLinked to original sources

arXiv2026

Boost-invariant and cylindrically symmetric perfect spin hydrodynamics

Equations of a boost-invariant and cylindrically symmetric perfect hydrodynamics are solved numerically for initial conditions inspired by the wounded nucleon model. The energy-momentum and spin tensors are used in the form that describes a relativistic massive gas governed by Boltzmann statistics. In contrast to one dimensional boost-invariant expansion, we find a coupling between the azimuthal and longitudinal components of the electric and magnetic components of the spin polarization tensor. This feature is similar to that found earlier for the Gubser symmetry, however, our treatment allows for a more general form of initial conditions and expansion geometry. Defining the freeze-out hypersurface by the constant temperature condition, we evaluate the Pauli-Lubański four-vector and find that for the assumed geometry the only nonzero total polarization may be induced by the longitudinal component of the magnetic part of the spin polarization tensor coupled with the azimuthal electric component. The obtained results may serve as a reference point for more realistic models of hydrodynamic expansion.

hep-ph↗

arXiv2026

Hyperon longitudinal polarization and vector meson spin alignment in a thermal model for heavy-ion collisions

The concept of a common local spin equilibrium for both spin-1/2 and spin-1 particles is incorporated into a thermal model of particle production in heavy-ion collisions at the top RHIC energies. We show that an effective spin polarization tensor leading to a correct description of the longitudinal spin polarization of $Λ$ hyperons simultaneously yields a positive alignment of vector mesons ($ϕ$ and $K^{*0}$) that grows monotonically with transverse momentum and centrality. Similar trends can be seen in the data, suggesting a possible common mechanism for longitudinal spin polarization and alignment. However, model calculations are insufficient to explain the data in a fully quantitative way. The correlation found between the magnitude of the $Λ$ longitudinal polarization and vector meson alignment suggests further more elaborate investigations of this issue.

hep-ph↗

arXiv2026

Spin alignment, tensor polarizabilities, and local equilibrium for spin-1 particles

Different bases for the spin-1 density matrix are discussed to clarify the connection between its components and observables measured in heavy-ion collisions. The theoretical advantage of using the adjoint representation for spin matrices is emphasized. Next, the equilibrium spin density matrix and the corresponding Wigner function are introduced. With appropriate definitions of the energy-momentum and spin tensors, this framework allows for the formulation of perfect spin hydrodynamics in the same way as previously done for spin-1/2 particles. Together, these results provide a unified description of spin-1/2 and spin-1 particles.

nucl-th↗

arXiv2025

Nonlinear causality and stability of perfect spin hydrodynamics and its nonperturbative character

Four formulations of perfect spin hydrodynamics for spin-1/2 particles, distinguished by their treatment of spin (classical vs. quantum) and by the underlying particle statistics (Boltzmann vs. Fermi-Dirac), are analyzed and shown to satisfy the requirements of a divergence-type theory. Moreover, for all the formulations, we define the generating functions associated with the relevant thermodynamic currents and demonstrate that the constructed hydrodynamic theory is nonlinearly causal and stable. The latter is achieved by employing the exact expressions for the distribution functions, indicating a nonperturbative character of our approach.

hep-ph↗

arXiv2025

Local equilibrium Wigner function for spin-1/2 particles

Formal connections between the spin density matrix and the Wigner function for spin-1/2 particles forming a relativistic gas are explored to determine their general structures. They suggest that the commonly used form of the local equilibrium Wigner function should be replaced by a new expression. The latter fulfills the necessary condition for the normalization of the mean spin polarization, which the former fails to reproduce. The new definition of the Wigner function leads to generalized thermodynamic relations for perfect spin hydrodynamics, identical to those obtained earlier using the classical concept of spin. Moreover, one can prove that the perfect spin hydrodynamics based on the new equilibrium Wigner function is nonlinearly causal and stable. Finally, the selection rule for the Lagrange multipliers, which is satisfied by real systems, is discussed.

hep-ph↗

arXiv2025

Exact Wigner function for chiral spirals

The exact solution of the Dirac equation for fermions coupled to an external periodic chiral condensate (chiral spiral) is used to obtain the exact formula for the Wigner function (up to the quantum loop corrections). We find that the resulting expressions for various coefficients of the Wigner function exhibit properties that cannot be reproduced within the standard semiclassical expansion. The formula for the axial vector component of the Wigner function can be conveniently used to study spin polarization effects and illustrate connections between the spin density matrix and axial current. In particular, we find that during an adiabatic change of the periodic potential into a uniform one, the polarization vector is twisted from its original direction.

hep-ph↗

arXiv2025

Spin hydrodynamics -- recent developments

After briefly touching on relativistic hydrodynamics, we provide a detailed description of recent developments in spin hydrodynamics. We discuss the theory of perfect spin hydrodynamics within two different approaches, which lead to identical generalized thermodynamic relations. We also indicate the applicability range of the theory, finding it compatible with the conditions existing in the late stages of heavy-ion collisions. Finally, we discuss the near-equilibrium dynamics.

hep-ph↗

arXiv2025

Application range of perfect spin hydrodynamics

The application range of perfect spin hydrodynamics is studied in two cases: one based on the classical spin description and the other using a quantum spin density matrix (Wigner function). Different forms of the conditions connecting the components of the spin polarization tensor, particle mass, temperature, and hydrodynamic flow are introduced, and their mutual relations are explained. The results obtained are important for practical applications of spin hydrodynamics to model heavy-ion collisions.

hep-ph↗

arXiv2025

$^3$H and $^3$He nuclei production in a combined thermal and coalescence framework for heavy-ion collisions in the few-GeV energy regime

A thermal model describing hadron production in heavy-ion collisions in the few-GeV energy regime is combined with the idea of nucleon coalescence to make predictions for the $^3$H and $^3$He nuclei production. A realistic parametrization of the freeze-out conditions is used, which reproduces well the spectra of protons and pions. It also correctly predicts the deuteron yield that agrees with the experimental value. The predicted yields of $^3$H and $^3$He appear to be smaller by about a factor of two compared to the experimental results. The model predictions for the spectra can be compared with future experimental data.

hep-ph↗

arXiv2025

Spin dynamics with realistic hydrodynamic background for relativistic heavy-ion collisions

The equations of perfect spin hydrodynamics are solved for the first time using a realistic (3+1)-dimensional hydrodynamic background, calibrated to reproduce a comprehensive set of hadronic observables, including rapidity distributions, transverse momentum spectra, and elliptic flow coefficients for Au+Au collisions at the beam energy of $\sqrt{s_{\rm NN}} = 200$ GeV. The spin dynamics is governed by the conservation of the spin tensor, describing spin-$\frac{1}{2}$ particles, with particle mass in the spin tensor treated as an effective parameter. We investigate several scenarios, varying both the effective mass and the initial evolution time for the spin polarization tensor. The model predictions are then compared with experimental measurements of global and longitudinal spin polarization of Lambda hyperons. Our results indicate that a successful description of the data requires a delayed initial evolution time for the perfect spin hydrodynamics of about 4 fm/$c$ (in contrast to the standard initial time of 1 fm/$c$ used for the hydrodynamic background). This delay marks a transition from the phase where spin-orbit interaction is significant to the regime where spin-conserving processes dominate. Our findings suggest that the spin-orbit dissipative interaction plays a significant role only in the very early stages of the system's evolution.

hep-ph↗

arXiv2025

Dynamical constraints on pseudo-gauge transformations

Classical pseudo-gauge transformations are discussed in the context of hydrodynamic models of heavy-ion collisions. A decomposition of the pseudo-gauge transformation into Lorentz-invariant tensors is made, which allows for better interpretation of its physical consequences. For pseudo-gauge transformations connecting two symmetric energy-momentum tensors, we find that the super-potential $Φ^{λμν}$ must obey a conservation law of the form $\partial_λΦ^{λμν} = 0$. This equation, referred to below as the STS condition, represents a constraint that is hardly possible to be satisfied for tensors constructed out of the basic hydrodynamic variables such as temperature, baryon chemical potential, and the hydrodynamic flow. However, in a special case of the boost-invariant flow, the STS condition is automatically fulfilled and a non-trivial residual pseudo-gauge transformation defined by a single scalar field is allowed. In this case the bulk and shear viscosity coefficients become pseudo-gauge dependent; however, their specific linear combination appearing in the equations of motion remains pseudo-gauge invariant. This finding provides new insights into the role of pseudo-gauge transformations and pseudo-gauge invariance.

hep-ph↗

arXiv2024

Hybrid approach to perfect and dissipative spin hydrodynamics

A hybrid framework of spin hydrodynamics is proposed that combines the results of kinetic theory for particles with spin 1/2 with the Israel-Stewart method of introducing nonequilibrium dynamics. The framework of kinetic theory is used to define the perfect-fluid description that conserves baryon number, energy, linear momentum and spin part of angular momentum. This leads to the entropy conservation although, in the presence of spin degrees of freedom, the perfect-fluid formalism includes extra terms whose structure is usually attributed to dissipation. The genuine dissipative terms appear from the condition of positive entropy production in nonequilibrium processes. They are responsible for the transfer between the spin and orbital parts of angular momentum, with the total angular momentum being conserved.

hep-ph↗

arXiv2024

Spin hydrodynamics

The concept of spin hydrodynamics is reexamined and briefly characterized.

hep-ph↗

arXiv2024

Boost-invariant spin hydrodynamics with spin feedback effects

A recently formulated extension of perfect spin hydrodynamics, which includes second-order corrections in the spin polarization tensor to the energy-momentum tensor and baryon current, is studied in the case of a one-dimensional boost-invariant expansion. The presence of second-order corrections introduces feedback from spin dynamics on the hydrodynamic background, constraining possible spin polarization configurations. However, as long as the magnitude of the spin polarization tensor remains small (below unity in natural units), the permitted spin dynamics differs very little from that found in the case without the second-order corrections.

hep-ph↗

arXiv2024

Energy-momentum correlators of fermions at finite temperature and density

Equal-time commutators of different components of the energy-momentum tensor at spatially separated points are calculated for a relativistic quantum Fermi gas at finite temperature and density. Different definitions of such components, also known as different pseudogauges, are used and smeared with a Gaussian profile characterized by the width $σ$. In this way, we introduce observables that may represent measurements of energy and momentum in a spatial region of size $σ$. We find that the obtained commutators are sensitive to the pseudogauge chosen if the probed systems or the spatial separation are small. The pseudogauge dependence is expected as different quantum operators are analyzed in this case. On the other hand, we find that for sufficiently large probed systems or with large separation, the studied commutators are pseudogauge independent.

hep-ph↗

arXiv2024

Lambda transverse polarization in NA61\SHINE at the CERN SPS: feasibility studies

The spin polarization of $Λ$ hyperons produced in inclusive reactions with unpolarized protons on unpolarized targets has been studied for almost 40 years. The NA61\SHINE experiment at the CERN SPS has a great potential to study transverse polarization in p-p and p-A collisions. In this work, we discuss the impact of magnetic field and limited detector acceptance on the possible polarization measurement by this experiment. Our analysis shows that the magnetic field impact on the $Λ$ polarization due to precession is one order of magnitude smaller than the detector acceptance-based polarization bias, and the identification of an experimental signal similar to that observed before by other experiments is possible.

hep-ph↗

arXiv2024

Generalized thermodynamic relations for perfect spin hydrodynamics

Generalized thermodynamic relations are introduced into the framework of a relativistic perfect spin hydrodynamics. They allow for consistent treatment of spin degrees of freedom, including the use of spin tensors whose structure follows from microscopic calculations. The obtained results are important for establishing consistency between different formulations of spin hydrodynamics and form the basis for introducing dissipative corrections.

hep-ph↗

arXiv2024

Stability and causality of rest frame modes in second-order spin hydrodynamics

We analyze the low- and high-momentum rest frame modes in the second-order spin hydrodynamics and check the asymptotic causality of the theory. A truncation scheme of the Israel-Stewart formalism derived in our earlier work is proposed that extends the minimal causal formulation. It consists of altogether 40 interconnected relaxation-type dynamical equations -- 16 (24) of them correspond to the independent components of the energy-momentum (spin) tensor. Similarly to previous studies, we find that the stability of the perturbations and asymptotic causality require using the spin equation of state that satisfies the generalized Frenkel condition demanding that the ``electric'' and ``magnetic'' components of the spin density tensor have opposite signs. For low-momentum modes this behavior is similar to that found earlier for the first-order (Navier-Stokes) spin hydrodynamics.

hep-ph↗