Abstract
We derive Kubo formulae for first-order spin hydrodynamics based on non-equilibrium statistical operators method. In first-order spin hydrodynamics, there are two new transport coefficients besides the ordinary ones appearing in first-order viscous hydrodynamics. They emerge due to the incorporation of the spin degree of freedom into fluids and the spin-orbital coupling. Zubarev's non-equilibrium statistical operator method can be well applied to investigate these quantum effects in fluids. The Kubo formulae, based on the method of non-equilibrium statistical operators, are related to equilibrium (imaginary-time) infrared Green's functions, and all the transport coefficients can be determined when the microscopic theory is specified.
Highlights
Recent developments in relativistic heavy-ion collisions have seen great progress in studying observables with spin dependence
We focus on small perturbations around the equilibrium system, that is, the thermodynamic forces can be treated as perturbations
We have evaluated Kubo formulae for transport coefficients arising in first-order spin hydrodynamics based on the approach of the nonequilibrium statistical operator
Summary
Recent developments in relativistic heavy-ion collisions have seen great progress in studying observables with spin dependence. The measurements of spin polarization of Λ hyperons show that a fraction of the spin of quarks within the hyperons takes one particular direction [1,2], which implies the media, quark-gluon plasma (QGP), should carry a large magnitude of angular momentum. One promising framework is hydrodynamics with the spin degree of freedom included In other words, these direct experimental measurements of quantum effects in relativistic heavy-ion collisions motivate the incorporation of the quantum spin degree of freedom into the evolution of fluids. We utilize the nonequilibrium statistical operator method developed by Zubarev [26,27,28] to derive Kubo formulae for transport coefficients of relativistic spinful fluids. We employ the symmetric/antisymmetric shorthand notations: XðμνÞ ≡ ðXμν þ XνμÞ=2; ð1Þ
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