de Haas-van Alphen effect in canonical and grand canonical multiband Fermi liquid

A qualitatively different character of de Haas-van Alphen oscillations has been found in a multiband (quasi)two-dimensional Fermi liquid with a fixed fermion density n(e) (canonical ensemble) compared with an open system where the chemical potential mu is kept fixed (grand canonical ensemble). A new fundamental period P-f appears when n(e) is fixed, a damping of the Landau levels is relatively small and a background density of states is negligible. P-f is determined by the total density rather than by the partial densities of carriers in different bands: P-f = 1/2n(e) phi for spin-split Landau levels and P-f = 1/n(e) phi in the case of spin degenerate levels where phi is the flux quantum.