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A new gauge fixing condition is discussed, which is (lattice) rotation invariant, has the 'smoothness' properties of the Landau gauge but can be efficiently computed and is unambiguous for almost all lattice gauge field configurations. * on leave from HLRZ c/o KFA Jülich,

We investigate a recent proposal to construct chiral gauge theories on the lattice using domain wall fermions. We restrict ourselves to the finite volume case, in which two domain walls are present, with modes of opposite chirality on each of them. We couple the chiral fermions on only one of the domain walls to a gauge field. In order to preserve gauge invariance, we have to add a scalar field, which gives rise to additional light mirror fermion and scalar modes. We argue that in an anomaly-free model these extra modes would decouple if our model possesses a so-called strong coupling symmetric phase. However, our numerical results indicate that such a phase most probably does not exist.PACS number(s): 11.15.Ha. 12.38.G~

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For homogeneous initial conditions, Hartree (gaussian) dynamical approximations are known to have problems with thermalization, because of insufficient scattering. We attempt to improve on this by writing an arbitrary density matrix as a superposition of gaussian pure states and applying the Hartree approximation to each member of such an ensemble. Particles can then scatter via their back-reaction on the typically inhomogeneous mean fields. Starting from initial states which are far from equilibrium we numerically compute the time evolution of particle distribution functions and observe that they indeed display approximate thermalization on intermediate time scales by approaching a Bose-Einstein form. However, for very large times the distributions drift towards classical-like equipartition.11.15.Ha, 11.10.Wx