Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator
Physics Department, Cinvestav, A.P. 14-740, 07000, Mexico City, Mexico
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Revised: 29 March 2016
Accepted: 11 April 2016
Published online: 17 May 2016
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.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016