Domain shape dependence of semiclassical corrections to energy

TL;DR

This paper investigates how the size and boundary conditions of a finite domain influence semiclassical energy corrections for static kink solutions in a multidimensional Sine-Gordon system.

Contribution

It introduces a detailed analysis of the domain shape and boundary effects on semiclassical energy corrections in a multidimensional setting.

Findings

Semiclassical corrections depend significantly on domain size and boundary conditions.

Rectangular cross-section domains exhibit specific energy correction behaviors.

Boundary choices impact the stability and energy estimates of kink solutions.

Abstract

Stationary solution of one-dimensional Sine-Gordon system is embedded in a multidimensional theory with explicitly finite domain in the added spatial dimensions. Semiclassical corrections to energy are calculated for static kink solution with emphasis on the impact of scale of the domain as well as the choice of boundary conditions on the results for rectangular cross-section.