New scenarios for classical and quantum mechanical systems with position dependent mass

TL;DR

This paper explores systems with position-dependent mass derived from higher-dimensional theories, revealing new models of nonlinear oscillators coupled to dilaton fields with potential applications in string theory.

Contribution

It introduces a novel origin of position-dependent mass from inhomogeneous Kaluza-Klein compactification and extends solutions to include dilaton field interactions.

Findings

Generalized nonlinear oscillator models with PDM due to dilatonic coupling

Extended solutions interpreted as particles interacting with dilaton fields

Application to nonlinear oscillators coupled to dilatonic strings

Abstract

An inhomogeneous Kaluza-Klein compactification to four dimensions, followed by a conformal transformation, results in a system with position dependent mass (PDM). This origin of a PDM is quite different from the condensed matter one. A substantial generalization of a previously studied nonlinear oscillator with variable mass is obtained, wherein the position dependence of the mass of a nonrelativistic particle is due to a dilatonic coupling function emerging from the extra dimension. Previously obtained solutions for such systems can be extended and reinterpreted as nonrelativistic particles interacting with dilaton fields, which, themselves, can have interesting structures. An application is presented for the nonlinear oscillator, where within the new scenario the particle is coupled to a dilatonic string.