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03 November 2024
 
  » arxiv » hep-th/9303004

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Symmetries of the Self-Similar Potentials
V.Spiridonov ;
Date 1 Mar 1993
Subject hep-th
AbstractAn application of the particular type of nonlinear operator algebras to spectral problems is outlined. These algebras are associated with a set of one-dimensional self-similar potentials, arising due to the q-periodic closure f_{j+N}(x)=qf_j(qx), k_{j+N}=q^2 k_j of a chain of coupled Riccati equations (dressing chain). Such closure describes q-deformation of the finite-gap and related potentials. The N=1 case corresponds to the q-oscillator spectrum generating algebra. At N=2 one gets a q-conformal quantum mechanics, and N=3 set of equations describes a deformation of the Painleve IV transcendent.
Source arXiv, hep-th/9303004
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