Speaker
Description
Collective coordinate models reduce field dynamics to a few variables, but their accuracy depends strongly on the ansatz. I will discuss a sequence of examples in which the kink profile is adapted to the local geometry or to spatially and temporally varying coefficients. Starting with radial $\phi^4$ kinks in a Schwarzschild-like geometry, I will show how a metric dependent rescaling combined with a dynamical width gives an accurate reduced description beyond the weak gravity regime. I will then consider sine-Gordon kinks on periodic and non-autonomous backgrounds, where the local background enters directly into a two-coordinate ansatz for the kink position and width. The resulting models reproduce long and nontrivial field trajectories and can also be used to analyse parametrically driven instabilities. Finally, I will discuss the extension to a driven damped $\phi^4$ model and compare width based and internal mode based reductions. These examples show that the structure built into the ansatz, especially the local scale imposed by the background, is often as important as the choice of collective coordinates themselves.