On First Order Green Function Theory with Spin Operators

Seiichiro Katsura, T. Horiguchi

G. Kamieniarz

Jin Chun Hu

We derive Kubo formulae for first-order spin hydrodynamics based on nonequilibrium 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 nonequilibrium statistical operator method can be well applied to investigate these quantum effects in fluids. The Kubo formulae, based on the method of nonequilibrium 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.

D. I. Kadyrov

Izyumov, Chashchin

For a tJ -model in the X -operators representation a generating functional of the field describing fluctuations of matrix elements of electron hopping on a lattice is presented.The first order functional derivative with respect to this field determines the electron Green function, while the second order derivatives determine the boson Green functions of collective excitations in the system.Thus, the Kadanoff-Baym approach in the theory of fermi system with a weak Coulomb interaction is generalized on the opposite limit of systems with strong correlations.A chain of equations for different order variational derivatives were obtained, and a method was suggested based on iterations over the parameters of a tJ -model: the hopping matrix element and the exchange integral.This approach corresponds to a self-consistent Born approximation, not for the effective but for the original Hamiltonian.A scheme of calculation of the dynamical spin susceptibility is analyzed with self-consistent corrections of the first and second order.Connection of this approach with the diagram technique for X -operators is discussed.

Bi Qiao, Harry E. Ruda