"Stringy" Coherent States Inspired By Generalized Uncertainty Principle

TL;DR

This paper constructs generalized coherent states for a non-commutative harmonic oscillator satisfying the GUP, revealing fractional revivals and setting bounds on the minimal length scale with sub-Poissonian statistics.

Contribution

It introduces explicit GUP-compatible coherent states for the non-commutative harmonic oscillator with a smooth commutative limit, and analyzes their quantum statistical properties.

Findings

States exhibit fractional revival phenomena.

Provides an independent bound on the GUP parameter.

Determines the maximum GUP-induced minimal length scale.

Abstract

In this Letter we have explicitly constructed Generalized Coherent States for the Non-Commutative Harmonic Oscillator that directly satisfy the Generalized Uncertainty Principle (GUP). Our results have a smooth commutative limit. The states show fractional revival which provides an independent bound on the GUP parameter. Using this and similar bounds we derive the largest possible value of the (GUP induced) minimum length scale. Mandel parameter analysis shows that the statistics is Sub-Poissionian.