Long-time tails of the heat-conductivity time correlation functions for a magnetized plasma: A kinetic-theory approach

The long-time behaviour of the longitudinal and the transverse heat-conductivity time correlation functions for a magnetized one-component plasma is studied by means of kinetic theory. To that end these correlation functions, which are defined as the inverse Laplace transforms of the dynamic heat conductivity coefficients, are expressed in terms of matrix elements of the kernel that appears in the kinetic equation for the phase-space density time correlation function. The explicit expression for the collision kernel in the disconnected approximation is used to write the dominant contributions to the heat-conductivity time correlation functions for large t as integrals over products of reduced time correlation functions for the particle density, the momentum density and the kinetic-energy density. By substituting the asymptotic expressions for the latter the decay of the long-time tails of the heat-conductivity time correlation functions is found to be proportional to t−12. Hence, the results obtained by this kinetic approach corroborate the t−12-tails of the Green-Kubo integrands for the heat conductivities that have been derived previously with the help of mode-coupling theory.