Thermal and quantum fluctuations around domain walls

Abstract

We compute thermal and quantum fluctuations in the background of a domain wall in a scalar field theory at finite temperature using the exact scalar propagator in the subspace orthogonal to the wall's translational mode. The propagator makes it possible to calculate terms of any order in the semiclassical expansion of the partition function of the system. The leading term in the expansion corresponds to the fluctuation determinant, which we compute for arbitrary temperature in space dimensions $1,$ $2,$ and $3.$ Our results may be applied to the description of thermal scalar propagation in the presence of soliton defects (in polymers, magnetic materials, etc.) and interfaces which are characterized by kinklike profiles. They lead to predictions as to how classical free energy differences, surface tensions, and interface profiles are modified by fluctuations, allowing for comparison with both numerical and experimental data. They can also be used to estimate transition temperatures. Furthermore, the simple analytic form of the propagator may simplify existing calculations, and allow for more direct comparisons with data from scattering experiments.