High Energy Physics - Theory
[Submitted on 31 Dec 2015 (v1), last revised 20 Apr 2016 (this version, v3)]
Title:Position-dependent mass, finite-gap systems, and supersymmetry
View PDFAbstract: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 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 Lame 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 AdS_2-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.
Submission history
From: Mikhail Plyushchay [view email][v1] Thu, 31 Dec 2015 05:55:09 UTC (2,143 KB)
[v2] Tue, 12 Jan 2016 03:29:26 UTC (2,144 KB)
[v3] Wed, 20 Apr 2016 03:22:49 UTC (2,145 KB)
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