arXiv subjects

Sudip Kumar Kar

Publications and source records attributed to Sudip Kumar Kar.

6 recordsLinked to original sources

arXiv2026

Constructing perfect spin-1 hydrodynamics from Boltzmann to Bose-Einstein statistics

We derive thermodynamic currents for a perfect fluid of massive spin-1 particles obeying Bose-Einstein statistics within the Wigner-function approach. Using a covariant spin density matrix, we construct spin-extended equilibrium distributions and obtain the energy-momentum and spin tensors that match, up to second order in polarization, those of spin-1/2 systems and the Boltzmann case. We find that the approach yields a unified description of relativistic spin hydrodynamics independent of statistics and spin representation. Furthermore, the framework fulfills the requirements of the divergence-type theory, with nonlinearly causal and stable dynamical equations.

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

Fermi-Dirac Wigner function for massive spin-1/2 particles in local equilibrium

A recently proposed Boltzmann local equilibrium Wigner function for massive spin-1/2 particles is generalized to the case of Fermi-Dirac statistics. The resulting formula ensures the correct normalization of the mean polarization vector and reproduces the generalized thermodynamic relations with spin that were obtained in earlier studies. Moreover, we show that the macroscopic currents constructed from the Fermi-Dirac Wigner function can be obtained as derivatives of a suitably defined generating function with respect to the Lagrange multipliers (temperature, hydrodynamic flow, and chemical potentials). The identified generating function also indicates that the underlying framework can be classified as a divergence-type theory.

quant-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↗