On the Stability of Coherent States for Pais-Uhlenbeck Oscillator

Abstract

We have constructed coherent states for the higher derivative Pais-Uhlenbeck Oscillator. In the process we have suggested a novel way to construct coherent states for the oscillator having only negative energy levels. These coherent states have negative energies in general but their coordinate and momentum expectation values and dispersions behave in an identical manner as that of normal (positive energy) oscillator. The coherent states for the Pais-Uhlenbeck Oscillator have constant dispersions and a modified Heisenberg Uncertainty Relation. Moreover, under reasonable assumptions on parameters these coherent states can have positive energies.

Title changed, modified version with no major change in results and conclusions, to appear in Mod.Phys.Lett. A

References in corpus (4)

• Making Sense of Non-Hermitian Hamiltonians
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• "Stringy" Coherent States Inspired By Generalized Uncertainty Principle
• Coherent States for the Non-Linear Harmonic Oscillator

Cited by in corpus (6)

• Pais-Uhlenbeck Oscillator and Negative Energies
• On Negative Energies, Strings, Branes, and Braneworlds: A Review of Novel Approaches
• Entanglement of higher-derivative oscillators in holographic systems
• Generalized Niederer's transformation for quantum Pais-Uhlenbeck oscillator
• Nonlocal dynamics and infinite non-relativistic conformal symmetries
• New (Ghost-Free) Formulation of the Pais-Uhlenbeck Oscillator