On Hamiltonians with position-dependent mass from Kaluza-Klein compactifications

TL;DR

This paper explores how inhomogeneous Kaluza-Klein compactifications can generate position-dependent mass systems with radial symmetry, linking extra-dimensional geometry to dynamical properties and curvature in four-dimensional physics.

Contribution

It extends previous work by providing new examples of PDM systems from Kaluza-Klein compactifications with radial symmetry and discusses their geometric and dynamical implications.

Findings

Generated PDM systems with radial symmetry from compactifications

Compared properties of extra dimensions with nonlinear oscillator models

Proposed a new mechanism for dynamical curvature generation

Abstract

In a recent paper (J.R. Morris, Quant. Stud. Math. Found. 2 (2015) 359), an inhomogeneous compactification of the extra dimension of a five-dimensional Kaluza-Klein metric has been shown to generate a position-dependent mass (PDM) in the corresponding four-dimensional system. As an application of this dimensional reduction mechanism, a specific static dilatonic scalar field has been connected with a PDM Lagrangian describing a well-known nonlinear PDM oscillator. Here we present more instances of this construction that lead to PDM systems with radial symmetry, and the properties of their corresponding inhomogeneous extra dimensions are compared with the ones in the nonlinear oscillator model. Moreover, it is also shown how the compactification introduced in this type of models can alternatively be interpreted as a novel mechanism for the dynamical generation of curvature.