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Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator

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Abstract.

Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.

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Authors and Affiliations

  1. Physics Department, Cinvestav, A.P. 14-740, 07000, Mexico City, Mexico

    Erik Díaz-Bautista & David J. Fernández Cabrera

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  1. Erik Díaz-Bautista
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  2. David J. Fernández Cabrera
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Correspondence to Erik Díaz-Bautista.

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Díaz-Bautista, E., Fernández Cabrera, D. Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator. Eur. Phys. J. Plus 131, 151 (2016). https://doi.org/10.1140/epjp/i2016-16151-2

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  • DOI: https://doi.org/10.1140/epjp/i2016-16151-2

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