Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations

Dey, S. & Fring, A. (2012). Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations. Physical Review D - Particles, Fields, Gravitation and Cosmology, 86(6), doi: 10.1103/PhysRevD.86.064038

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Abstract

We provide an explicit construction for Gazeau-Klauder coherent states related to non-Hermitian Hamiltonians with discrete bounded below and nondegenerate eigenspectrum. The underlying spacetime structure is taken to be of a noncommutative type with associated uncertainty relations implying minimal lengths. The uncertainty relations for the constructed states are shown to be saturated in a Hermitian as well as a non-Hermitian setting for a perturbed harmonic oscillator. The computed value of the Mandel parameter dictates that the coherent wave packets are assembled according to sub-Poissonian statistics. Fractional revival times, indicating the superposition of classical-like sub-wave packets, are clearly identified.

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