Squeezed coherent states for noncommutative spaces with minimal length uncertainty relations

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 wavepackets are assembled according to sub-Poissonian statistics. Fractional revival times, indicating the superposition of classical-like sub-wave packets are clearly identified.

14 pages, 2 figures

References in corpus (23)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• String Theory and Noncommutative Geometry
• Making Sense of Non-Hermitian Hamiltonians
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• The quantum structure of spacetime at the Planck scale and quantum fields
• Pseudo-Hermitian Representation of Quantum Mechanics
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
• Noncommutative Geometry and Gravity
• Temporally stable coherent states for infinite well and Pöschl-Teller potentials
• Minimal length, maximal momentum and Hilbert space representation of quantum mechanics
• The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field
• Minimal length in Quantum Mechanics and non-Hermitian Hamiltonian systems
• Position-dependent noncommutativity in quantum mechanics
• On the Minimal Length Uncertainty Relation and the Foundations of String Theory
• PT-symmetric noncommutative spaces with minimal volume uncertainty relations
• "Stringy" Coherent States Inspired By Generalized Uncertainty Principle
• Strings from position-dependent noncommutativity
• Minimal areas from q-deformed oscillator algebras
• Complexified coherent states and quantum evolution with non-Hermitian Hamiltonians
• Snyder Noncommutativity and Pseudo-Hermitian Hamiltonians from a Jordanian Twist
• Minimum-length deformed quantization of a free field on de Sitter background and corrections to the inflaton perturbations

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