Novel connection between lump-like structures and quantum mechanics

TL;DR

This paper explores the connection between lump-like structures in scalar field models and quantum mechanics, revealing new stable solutions and potential shapes relevant to quantum systems.

Contribution

It introduces a deformation method to generate models with lump and kink solutions, linking classical field configurations to quantum mechanical potentials.

Findings

Models support stable topological solutions with non-negative bound states.

Stability potentials can form double-well shapes.

New physical systems with tower of bound states are identified.

Abstract

This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar field theories that support both lumps and kinks, with the corresponding stability investigation giving rise to new physical systems. Very interestingly, we find models that support stable topological solutions, with the stability potential being able to support a tower of non-negative bound states, generating distinct families of potentials of current interest to quantum mechanics. We also describe models where the lump-like solutions give rise to stability potentials that have the shape of a double-well.