Small-wavenumber divergency in the mode-coupling amplitudes for the heat-current time correlation function of a dense one-component plasma in a magnetic field

The long-time behaviour of the heat-current time correlation function of a one-component plasma in a magnetic field is studied with the use of mode-coupling theory. The coupling of two gyro-plasmon modes gives rise to contributions with amplitudes that are divergent for small wavenumber. These imply a slowly decaying long-time tail of the Green-Kubo integrand. As such a behaviour would lead to a divergency in the static heat conductivity, it is concluded that mode-coupling theory with diverging coupling amplitudes is not a reliable starting point for the study of the long-time behaviour of Green-Kubo integrands.