  de Haas-van Alphen oscillation spectrum is studied for an idealized
two-dimensional Fermi liquid with two parabolic bands in the case of canonical
(fixed number of quasiparticles) and grand canonical (fixed chemical potential)
ensembles. As already reported in the literature, oscillations of the chemical
potential in magnetic field yield frequency combinations that are forbidden in
the framework of the semiclassical theory. Exact analytical calculation of the
Fourier components is derived at zero temperature and an asymptotic expansion
is given for the high temperature and low magnetic field range. A good
agreement is obtained between analytical formulae and numerical computations.
