Diamagnetic expansions for perfect quantum gases

In this work we study the diamagnetic properties of a perfect quantum gas in the presence of a constant magnetic field of intensity B. We investigate the Gibbs semigroup associated with the one particle operator at finite volume, and study its Taylor series with respect to the field parameter omega:=eB/c in different topologies. This allows us to prove the existence of the thermodynamic limit for the pressure and for all its derivatives with respect to omega (the so-called generalized susceptibilities). (c) 2006 American Institute of Physics.