Mixmaster Chaoticity as Semiclassical Limit of the Canonical Quantum Dynamics

TL;DR

This paper demonstrates that the chaotic behavior of the Mixmaster Universe near singularity can be understood as the semiclassical limit of its canonical quantum dynamics, linking classical chaos with quantum indeterminism.

Contribution

It provides a Hamiltonian analysis showing how classical chaos emerges from the semiclassical limit of quantum cosmological models.

Findings

Chaotic behavior is derived as the semiclassical limit of quantum dynamics.

The microcanonical and semiclassical quantum probability distributions coincide.

The analysis connects classical chaos with quantum indeterminism in cosmology.

Abstract

Within a cosmological framework, we provide a Hamiltonian analysis of the Mixmaster Universe dynamics on the base of a standard Arnowitt-Deser-Misner approach, showing how the chaotic behavior characterizing the evolution of the system near the cosmological singularity can be obtained as the semiclassical limit of the canonical quantization of the model in the same dynamical representation. The relation between this intrinsic chaotic behavior and the indeterministic quantum dynamics is inferred through the coincidence between the microcanonical probability distribution and the semiclassical quantum one.