Trapped mesoscopic quantum gas in a magnetic field

Feynman-type series for grand potential Ω, number of particles, internal energy, magnetization and susceptibility are derived for systems of noninteracting quantum particles in an external magnetic field. Numerical calculations at constant N for harmonically trapped systems of fermions and bosons in the presence of a homogeneous magnetic field are carried out with the aid of both Feynman-type series and series over single-particle states. N-convergence to universal curves for chemical potential and energy is presented. At low temperatures magnetization of the Fermi gas exhibits a pronounced quantum behaviour. (author)