Position-dependent mass, finite-gap systems, and supersymmetry

2015/12/31 by Rafael Bravo, Mikhail S. Plyushchay
Mathematics · Physics and Astronomy · #Angular momentum #Black Holes and Theoretical Physics #Classical mechanics #Dimensional reduction #Higgs boson #Kinetic term #Mathematical physics #Nonlinear Waves and Solitons #Nonlinear system #Physics #Position (finance) #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Supercharge #Supersymmetry #hep-th #math-ph #math.MP #nlin.SI #quant-ph

paper · pdf · doi:10.1103/physrevd.93.105023

published as Phys. Rev. D 93, 105023 (2016) · 35 pages, 7 figures; refs and comments added, version to appear in Phys. Rev. D

arxiv created 2016/04/20 · openalex publication_date 2016/05/16 · arxiv updated 2016/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The ordering problem in quantum systems with position-dependent mass (PDM) is treated by inclusion of the classically fictitious similarity transformation into the kinetic term. This provides a generation of supersymmetry with the first-order supercharges from the kinetic term alone, while inclusion of the potential term allows us also to generate nonlinear supersymmetry with higher-order supercharges. A broad class of finite-gap systems with PDM is obtained by different reduction procedures, and general results on supersymmetry generation are applied to them. We show that elliptic finite-gap systems of Lam'e and Darboux-Treibich-Verdier types can be obtained by reduction to Seiffert's spherical spiral and Bernoulli lemniscate in the presence of Calogero-like or harmonic oscillator potentials, or by angular momentum reduction of a free motion on some AdS₂-related surfaces in the presence of Aharonov-Bohm flux. The limiting cases include the Higgs and Mathews-Lakshmanan oscillator models as well as a reflectionless model with PDM exploited recently in the discussion of cosmological inflationary scenarios.

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