Speaker
Description
The observation of spin polarization in non-central heavy-ion collisions has opened new directions in the development of relativistic hydrodynamic theories. Many theoretical frameworks have been developed to explain the phenomenon of polarization of the detected hadrons. One such framework is spin hydrodynamics, in which spin degrees of freedom, or equivalently the total angular momentum, are incorporated as hydrodynamic variables. In this approach, each fluid element is assumed to possess both orbital and spin angular momentum J=L+S. Consequently, the hydrodynamic evolution of such a fluid must satisfy the conservation of total angular momentum in addition to the usual conservation laws. In the present work, we consider dissipative spin hydrodynamics up to second order. Such second order theories are expected to be consistent with linear stability and causality constraints. The novelty of spin hydrodynamic framework is the presence of spin dissipations and spin transport coefficients.
Since the hydrodynamic variables can fluctuate from event to event around their ensemble-averaged values, these dissipations in energy-momentum as well as the spin tensor are accompanied by corresponding fluctuations according to the fluctuation-dissipation theorem. These hydrodynamic fluctuations are manifestations of thermal noise and must be incorporated to achieve a consistent event-by-event description of the dynamical evolution of the system. For small deviations from equilibrium, the non-equilibrium behavior is completely characterized by the corresponding correlation functions.
In this work, we investigate the hydrodynamic fluctuations associated with the second-order dissipative spin hydrodynamic theory. The spin chemical potential is treated as a leading-order term in the gradient expansion, and it affects the equation of state non-trivially. We derive the spin hydrodynamic equations of motion for minimally extended second-order spin hydrodynamics (Israel-Stewart form), as well as the Onsager coefficients associated with the noise correlators of the dissipative currents. For a boost-invariant system, the proper-time evolution of the conserved quantities and dissipative currents is obtained by solving the stochastic spin hydrodynamic equations using the Stratonovich integral algorithm. We show how fluctuations in the dissipative part of spin current evolve with proper time along with shear and bulk sector of the energy momentum tensor. This work establishes a novel, general framework for incorporating hydrodynamic fluctuations into spin hydrodynamics.
