Equilibrium fluctuations formulas for the quantum one-component plasma in a magnetic field

The authors derive a complete set of equilibrium fluctuation formulae for the charge density, the current density and the energy density of the quantum one-component plasma in a magnetic field. The derivation is based on the use of imaginary-time-dependent Green functions and their Kubo transforms. It is shown how the fluctuation formulae involving Kubo-transformed quantities can be established directly, even in the absence of a detailed knowledge of the full imaginary-time dependence of the Green functions. The resulting fluctuation formulae for the Kubo transforms are found to have a considerably simpler structure than those for the equal-imaginary-time observables.