Kink Localization under Asymmetric Double-Well Potential

TL;DR

This paper analyzes how asymmetric double-well potentials influence the localization of phase interfaces, revealing that the interface position depends solely on the second derivatives of the potential at minima, with applications in porous media and Brownian motors.

Contribution

It provides a general theoretical result on interface localization in asymmetric potentials and connects it to applications in porous media and physics of Brownian motors.

Findings

Interface position depends on second derivatives of potential at minima.

Asymmetry causes the interface to be non-symmetric and location-dependent.

Application to porous media shows relevance in solid-fluid segregation.

Abstract

We study diffuse phase interfaces under asymmetric double-well potential energies with degenerate minima and demonstrate that the limiting sharp profile, for small interface energy cost, on a finite space interval is in general not symmetric and its position depends exclusively on the second derivatives of the potential energy at the two minima (phases). We discuss an application of the general result to porous media in the regime of solid-fluid segregation under an applied pressure and describe the interface between a fluid-rich and a fluid-poor phase. Asymmetric double-well potential energies are also relevant in a very different field of physics as that of Brownian motors. An intriguing analogy between our result and the direction of the dc soliton current in asymmetric substrate driven Brownian motors is pointed out.