Novel connection between lump-like structures and quantum mechanics

Abstract

This work deals with lump-like structures in models described by a single real scalar field in twodimensional 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.

Scattering of metastable lumps in a model with a false vacuum

“…3. This potential can be separated in two regions from the value s = (1/2) ln( √ 3 + 2) ≃ 0.66 [33]. From s ≤ s the potential has a single-well, whereas for s > s the potential takes the shape of a double-well potential.…”

“…In some of these applications, the lump can be stabilized if described by a complex scalar field, as done in q-ball models [22], or coupled with other charged matter fields [23]. In this case the stable solution has a conserved Noether charge and is named by some authors as nontopological solitons.…”

Thick branes via higher order field theory models with exponential and power-law tails

“…In this way we are able to control important features of localized solutions, such as the kink amplitude, its rest mass and spatial scale, without any changes in the overall topological conditions. Using this method, one can also construct new topologies for the geometry of solitons [45], or transform non-topological lump-like structures of a specific field theory into a model supporting topological solutions [46,47].…”