The Polymer Bouncer
arXiv:1506.00183 · doi:10.1103/PhysRevD.92.045018
Abstract
Polymer Quantization (PQ) is a background independent quantization scheme that is deployed in Loop Quantum Gravity. This framework leads to a new short-distance (discretized) structure characterized by a fundamental length. In this paper we use PQ to analyze the problem of a particle bouncing on a perfectly reflecting surface under the influence of Earth's gravitational field, what we have called "\textit{The Polymer Bouncer}". In this scenario, deviations from the usual quantum effects are induced by the spatial discreteness, but not by a new short-range gravitational interaction. We solve the polymer Schrödinger equation in an analytical fashion, and we evaluate numerically the corresponding energy levels. We find that the polymer energy spectrum exhibits a negative shift compared to the obtained for the quantum bouncer. The comparison of our results with those obtained in the GRANIT experiment leads to an upper bound for the fundamental length scale, namely $λ\ll 0.6 \buildrel _{\circ} \over {\mathrm{A}}$. We find polymer corrections to the probability of transitions between levels, induced by small vibrations, together with the probability of spontaneous emission in the quadrupole approximation.
References in corpus (10)
- Neutron scattering and extra short range interactions
- Minimal Length Uncertainty Relation and gravitational quantum well
- Centrifugal quantum states of neutrons
- Propagators in Polymer Quantum Mechanics
- Polymer Bose--Einstein Condensates
- Spontaneous emission of graviton by a quantum bouncer
- Diffraction in Time of Polymer Particles
- Polymer quantization and Symmetries
- Macroscopic quantum behaviour of periodic quantum systems
- Transitions between levels of a quantum bouncer induced by a noise-like perturbation
Cited by in corpus (6)
- Local effects of the quantum vacuum in Lorentz-violating electrodynamics
- Casimir effect between ponderable media as modeled by the standard model extension
- Testing Lorentz- and CPT-invariance with ultracold neutrons
- Gravitational Searches for Lorentz Violation with Ultracold Neutrons
- Casimir effect in polymer scalar field theory
- Strong Equivalence Principle in Polymer Quantum Mechanics and deformed Heisenberg Algebra