Abstract

We present analytical methods to calculate the magnetic response of non-interacting electrons constrained to a domain with boundaries and submitted to a uniform magnetic field. Two different methods of calculation are considered-one involving the large energy asymptotic expansion of the resolvent (Stewartson-Waechter) applies to separable systems, the other based on the small time asymptotic behaviour of the heat kernel (Balian-Bloch). Both methods are in agreement with each other but differ from results previously obtained by Robnik. Finally, the Balian-Bloch multiple scattering expansion is studied and the extension of our results to other geometries is discussed.