Wide Class of Logarithmic Potentials with Power-Tower Kink Tails

TL;DR

This paper introduces a broad class of logarithmic potentials with diverse kink tail behaviors, including power-law, exponential, and power-tower tails, analyzing their stability and interactions.

Contribution

It develops a framework for constructing logarithmic potentials with complex kink tail structures and examines their stability and interaction properties.

Findings

Kinks exhibit various tail behaviors including power-law, exponential, and power-tower forms.

No spectral gap exists between zero modes and continuum in these models.

Provides a method to generate logarithmic potentials with specific kink tail configurations.

Abstract

We present a wide class of potentials which admit kinks and corresponding mirror kinks with either a power law or an exponential tail at the two extreme ends and a power-tower form of tails at the two neighbouring ends, i.e. of the forms $ette$ or $pttp$ where $e, p$ and $t$ denote exponential, power law and power-tower tail, respectively. We analyze kink stability equation in all these cases and show that there is no gap between the zero mode and the beginning of the continuum. Finally, we provide a recipe for obtaining logarithmic potentials with power-tower kink tails and estimate kink-kink interaction strength.