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

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.

11 pages, no figs; To appear in Quantum Stud: Math. Found

References in corpus (3)

• Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability
• Generalized dilaton-Maxwell cosmic string and wall solutions
• Reflection and transmission at dimensional boundaries

Cited by in corpus (5)

• Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach
• On Hamiltonians with position-dependent mass from Kaluza-Klein compactifications
• On the exactly-solvable semi-infinite quantum well of the non-rectangular step-harmonic profile
• Deformation of the Heisenberg-Weyl algebra and the Lie superalgebra $\mathfrak{osp}\left(1|2\right)$: exact solution for the quantum harmonic oscillator with a position-dependent mass
• Position-Dependent Mass Quantum systems and ADM formalism