Front propagation in non-homogeneous $\phi^4$ model

TL;DR

This paper studies how fronts propagate in an inhomogeneous $^4$ model, comparing effective kink-based descriptions with field-theory results, and proposes a modified model for better accuracy.

Contribution

It introduces a modified effective model that accurately reproduces field-theory results for front propagation in inhomogeneous media.

Findings

Effective kink description yields accurate results.

Half-kink approach shows significant deviations.

Modified model aligns well with field-theory predictions.

Abstract

We investigate the propagation of fronts in an inhomogeneous medium within the framework of the $\phi^4$ model. The inhomogeneity is modeled either as an interface separating regions with different dissipation or as a finite layer with modified dissipation. The propagating front is described in two ways: as a kink solution in an effectively unbounded domain, and as a half-kink in a finite system. The half-kink represents the decay of the unstable state $\phi=0$ toward the true vacuum. We show that while the effective description based on the kink provides accurate results, applying a similar approach to the half-kink leads to significant deviations from the predictions of the field model. We then demonstrate that a consistent description does exist and propose a modified effective model which reproduces the field-theory results over a relatively broad range of parameters.