TL;DR
This paper explores how classical chaos in the volume dynamics of a pentahedron influences the quantum spectrum, revealing a gap between zero and nonzero volumes, and linking chaos to quantum gravity's ultraviolet behavior.
Contribution
It provides a detailed analysis of pentahedral geometry, connects classical chaos to quantum spectral gaps, and offers new insights into the volume operator in quantum gravity.
Findings
Quantum spectra are gapped between zero and nonzero volume.
Classical chaos influences the quantum geometry spectrum.
New insights into the volume operator in quantum gravity.
Abstract
We show that chaotic classical dynamics associated to the volume of discrete grains of space leads to quantal spectra that are gapped between zero and nonzero volume. This strengthens the connection between spectral discreteness in the quantum geometry of gravity and tame ultraviolet behavior. We complete a detailed analysis of the geometry of a pentahedron, providing new insights into the volume operator and evidence of classical chaos in the dynamics it generates. These results reveal an unexplored realm of application for chaos in quantum gravity.
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