Abstract

We compute the high orders of the Weyl expansion for the heat kernel of a circle billiard in the presence of a uniform and perpendicular magnetic field. It is shown, in accordance with a conjecture made in Narevich et al (1998 J. Phys. A: Math. Gen. 31 4277), that some terms of this expansion can be identified with those of the Weyl expansion of a semi-infinite cylinder. The boundary correction to the Landau diamagnetic susceptibility of a non-degenerate electron gas in the billiard is determined.