  Using the supersymmetry approach, we study spectral statistical properties of
a two-dimensional quantum particle subject to a non-uniform magnetic field. We
focus mainly on the problem of regularisation of the field theory. Our analysis
begins with an investigation of the spectral properties of the purely classical
evolution operator. We show that, although the kinetic equation is formally
time-reversible, density relaxation is controlled by {\em irreversible}
classical dynamics. In the case of a weak magnetic field, the effective kinetic
operator corresponds to diffusion in the angle space, the diffusion constant
being determined by the spectral resolution of the inhomogeneous magnetic
field. Applying these results to the quantum problem, we demonstrate that the
low-lying modes of the field theory are related to the eigenmodes of the
irreversible classical dynamics, and the higher modes are separated from the
zero mode by a gap associated with the lowest density relaxation rate. As a
consequence, we find that the long-time properties of the system are
characterised by universal Wigner-Dyson statistics. For a weak magnetic field,
we obtain a description in terms of the quasi one-dimensional non-linear
$\sigma$-model.
