Topological defects are part of various physical systems, from superfluids and superconductors to gauge theories of elementary particles. Investigations of their rich dynamics are part of current research.
Experiments show that topological defects in form of vortices in clean two-dimensional superconductors move along with the supercurrent while in discrete superconducting Josephson-junction arrays they move perpendicular to it. Our numerical solutions of the Gross-Pitaevsky equation on fine and coarse grids, corresponding to the continuous and discrete systems respectively, correctly reproduce the qualitative behavior. This suggests that the discreteness itself is responsible for the phenomenon.
In brane-world scenarios, the [straight theta]-angle of the QCD vacuum can be interpreted as a constant current of topologically non-trivial instantons through the brane. If the topology of the bulk precludes such a current, it leads to a vanishing [straight theta]-angle and thereby to a solution of the Strong CP problem.
We present a low-dimensional example exhibiting these properties. A 1+1 dimensional Ising model with spatially dependent coupling plays the role of the gauge field in the bulk. A spontaneous symmetry breaking in the bulk allows transitions between states corresponding to different [straight theta]-angles on the pointlike brane, which gives the possibility for the [straight theta]-angle to vanish.
In a five-dimensional bulk the particle like instantons of QCD are gravitationally unstable and they collapse to a topologically charged black hole. Our numerical simulations of the collapse allow the study of the thermodynamic properties of the time-dependent black hole, in particular, they suggest a classical definition of free energy. The obtained results agree with the standard thermodynamics of static black holes.
