arXiv subjects

Radoslaw Ryblewski

Publications and source records attributed to Radoslaw Ryblewski.

At least 55 records · Page 3Linked to original sources

arXiv2020

Relaxation time approximation with pair production and annihilation processes

We extend the Boltzmann equation in the relaxation time approximation to explicitly include transitions between particles forming an interacting mixture. Using the detailed balance condition as well as conditions of energy-momentum and current conservation, we show that only two independent relaxation time scales are allowed in such an interacting system. Dissipative hydrodynamic equations and the form of transport coefficients is subsequently derived for this case. We find that the shear and bulk viscosity coefficients, as well as the baryon charge conductivity are independent of the transition time scale. However, the bulk viscosity and conductivity coefficients that can be attributed to the individual components of the mixture depend on the transition time.

hep-ph↗

arXiv2020

Correspondence between Israel-Stewart and first-order causal and stable hydrodynamics for Bjorken-expanding baryon-rich systems with vanishing particle masses

We obtain an exact correspondence between the dynamical equations in Israel-Stewart (IS) theory and first-order causal and stable (FOCS) hydrodynamics for a boost-invariant system with an ideal gas equation of state at finite baryon chemical potential. Explicit expressions for the temperature and chemical potential dependence of the regulators in the FOCS theory are given in terms of the kinetic coefficients and constant relaxation time of the IS theory. Using the correspondence between the IS and FOCS theory, stability conditions for a charged fluid which are known in the FOCS approach are applied and one finds that the IS theory considered is unstable.

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arXiv2020

Correspondence between Israel-Stewart and first-order casual and stable hydrodynamics for the boost-invariant massive case with zero baryon density

Exact correspondence between Israel-Stewart theory and first-order causal and stable hydrodynamics is established for the boost-invariant massive case with zero baryon density and the same constant relaxation times used in the shear and bulk sectors. Explicit expressions for the temperature dependent regulators are given for the case of a relativistic massive gas. The stability and causality conditions known in the first-order approach are applied and one finds that one of them is violated in this case.

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arXiv2020

Relativistic hydrodynamics for spin-polarized media

We summarize the key ingredients of the recently proposed formalism of relativistic perfect-fluid hydrodynamics with spin. Based on the underlying kinetic theory definitions for the equilibrium distribution functions we obtain the evolution equations governing the system's expansion. Employing Bjorken symmetry we study the spin polarization dynamics of the system.

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arXiv2020

Equivalence between first-order causal and stable hydrodynamics and Israel-Stewart theory for boost-invariant systems with a constant relaxation time

We show that the recently formulated causal and stable first-order hydrodynamics has the same dynamics as Israel-Stewart theory for boost-invariant, Bjorken expanding systems with a conformal equation of state and a regulating sector determined by a constant relaxation time. In this case, the general solution of the new first-order formulation can be determined analytically.

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arXiv2019

Spin chemical potential for relativistic particles with spin 1/2

We analyze algebraic structure of a relativistic semi-classical Wigner function of particles with spin 1/2 and show that it consistently includes information about the spin density matrix both in two-dimensional spin and four-dimensional spinor spaces. This result is subsequently used to explore various forms of equilibrium functions that differ by specific incorporation of spin chemical potential. We argue that a scalar spin chemical potential should be momentum dependent, while its tensor form may be a function of space-time coordinates only. This allows for the use of the tensor form in local thermodynamic relations. We furthermore show how scalar and tensor forms can be linked to each other.

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arXiv2019

Relativistic hydrodynamics for spin-polarized fluids

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.

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arXiv2019

Longitudinal spin polarization in a thermal model

We use a thermal model with single freeze-out to determine longitudinal polarization of $Λ$ 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.

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arXiv2019

Relativistic fluid dynamics and its extensions as an effective field theory

We examine hydrodynamics from the perspective of an effective field theory. The microscopic scale in this case is the thermalization scale, and the macroscopic scale is the gradient, with thermal fluctuations playing the role of $\hbar$. We argue that this method can be applied both, to consistently include thermal fluctuations in the theory, and to extend hydrodynamics to systems whose microscopic structure is non-trivial. For the latter, we discuss the case of spin polarization and gauge theories.

hep-th↗

arXiv2019

Spin polarization evolution in a boost invariant hydrodynamical background

Relativistic hydrodynamic equations for particles with spin one-half are used to determine the space-time evolution of the spin polarization in a boost-invariant and transversely homogeneous background. The hydrodynamic approach uses the forms of the energy-momentum and spin tensors based on de Groot, van Leeuwen, and van Weert formalism. Our calculations illustrate how the formalism of hydrodynamics with spin can be used to determine physical observables related to the spin polarization and how the latter can be compared with the experimental data.

hep-ph↗

arXiv2019

Relativistic fluid dynamics of spin-polarized systems of particles

We review basic ingredients of the recently introduced perfect-fluid hydrodynamic equations for particles with spin one-half. For a quasi-realistic setup, first numerical solutions for various hydrodynamic variables including the spin polarization tensor are presented. Our results indicate that the initial spin polarization of the hottest region may play a dominant role in the polarization of particles at freeze-out.

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arXiv2018

Dynamics of relativistic spin-polarized fluids

We briefly review the foundations of a new relativistic fluid dynamics framework for polarized systems of particles with spin one half. Using this approach we numerically study the dynamics of the spin polarization of a rotating medium resembling the ones created in high-energy heavy-ion collisions.

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arXiv2018

Fluid dynamics for relativistic spin-polarized media

We briefly review the basic features of a new framework for relativistic perfect fluid hydrodynamics of polarized systems consisting of particles with spin one half. Using this approach we numerically study the stability of a stationary vortex-like solution, representing global equilibrium of a rotating medium.

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arXiv2018

Thermodynamic versus kinetic approach to polarization-vorticity coupling

We critically compare thermodynamic and kinetic approaches, that have been recently used to study relations between the spin polarization and fluid vorticity in systems consisting of spin-one-half particles. The thermodynamic approach refers to general properties of global thermal equilibrium with a rigid-like rotation and demonstrates that the spin-polarization and thermal-vorticity tensors are equal. On the other hand, the kinetic approach uses the concept of the Wigner function and its semi-classical expansion. In most of the works done so far, the Wigner functions satisfy kinetic equations with a vanishing collision term. We show that this assumption restricts significantly applicability of such frameworks and, in contrast to many claims found in the literature, does not allow for drawing any conclusions regarding the relation between the thermal-vorticity and spin-polarization tensors, except for the fact that the two should be constant in global equilibrium. We further show how the kinetic-theory equations including spin degrees of freedom can be used to formulate a hydrodynamic framework for particles with spin. We define hydrodynamic equations starting separately from the formulation by de~Groot, van~Leeuwen, and van~Weert and from the canonical formalism. In the former case the energy-momentum tensor is symmetric and the spin tensor is conserved, while in the later case the energy-momentum tensor is not symmetric and the spin tensor is not conserved. Nevertheless, in the two cases the total angular momentum is always conserved. Interestingly, the two approaches are connected by the pseudo-gauge transformation, which we explicitly define.

hep-ph↗

arXiv2018

Convective stability of global thermodynamic equilibrium

We apply the convection stability criterion to a fluid in global thermodynamic equilibrium with a rigid rotation or with a constant acceleration along the streamlines. Different equations of state describing strongly interacting matter are considered and for each of them the analysed system is found to be stable with respect to convection. This finding brings new evidence for physical relevance of non-static global equilibrium states. Our results can be directly used for other similar media to check their convective stability.

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arXiv2018

Anisotropic hydrodynamic modeling of heavy-ion collisions at LHC and RHIC

In this proceedings contribution, we review 3+1d quasiparticle anisotropic hydrodynamics (aHydroQP). Then, we show some recent phenomenological comparisons between the aHydroQP model and some experimental results. We show comparisons between aHydroQP and Pb-Pb 2.76 TeV collisions from the ALICE collaboration and Au-Au 200 GeV collisions from RHIC experiments. We show that the quasiparticle anisotropic hydrodynamics model is able to describe the experimental results for Pb-Pb and Au-Au collisions quite well for many observables such as the spectra, multiplicity, elliptic flow, and HBT radii in many centrality classes.

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arXiv2018

Vortex-like solutions and internal structures of covariant ideal magnetohydrodynamics

We discuss a manifestly covariant formulation of ideal relativistic magnetohydrodynamics, which has been recently used in astrophysical and heavy-ion contexts, and compare it to other similar frameworks. We show that the covariant equations allow for stationary vortex-like solutions that represent generalizations of the perfect-fluid solutions describing systems in global equilibrium with rotation. Such solutions are further used to demonstrate that inhomogeneous Maxwell equations, implicitly included in the covariant framework, may generate very large electric charge densities. This suggests that solutions of the covariant formulation may violate in some cases the assumptions of standard ideal magnetohydrodynamics. Furthermore, we show that the flow four-vector and conserved currents obtained in the covariant approach are usually not related to each other, which hinders kinetic-theory interpretation of the obtained results.

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arXiv2017

Spin-dependent distribution functions for relativistic hydrodynamics of spin-1/2 particles

Recently advocated expressions for the phase-space dependent spin-1/2 density matrices of particles and antiparticles are analyzed in detail and reduced to the forms linear in the Dirac spin operator. This allows for a natural determination of the spin polarization vectors of particles and antiparticles by the trace of products of the spin density matrices and the Pauli matrices. We demonstrate that the total spin polarization vector obtained in this way agrees with the Pauli-Lubanski four-vector, constructed from an appropriately chosen spin tensor and boosted to the particle rest frame. We further show that several forms of the spin tensor used in the literature give the same Pauli-Lubanski four-vector.

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