An analytical formulation for phi^4 field-potential dynamics

TL;DR

This paper develops an analytical model for phi^4 field interactions with localized potentials, providing explicit formulas for how solitary solutions behave under barriers and wells, enhancing understanding of field-potential dynamics.

Contribution

It introduces a collective coordinate approach to analytically describe phi^4 field interactions with delta function potentials, bridging a gap between numerical and analytical methods.

Findings

Analytical expressions for field interactions with delta potentials.

Behavior of solitary solutions resembles point particles in complex potentials.

Field dynamics depend on initial conditions and potential parameters.

Abstract

An analytical model for adding a space dependent potential to the phi^4 field is presented, by constructing a collective coordinate for solitary solution of this model. Interaction of the $\phi^{4}$ field with a delta function potential barrier and also delta function potential well is investigated. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We will find that the behaviour of the solitary solution is like a point particle 'living' under the influence of a complicated potential which is a function of the field initial conditions and the potential parameters.