Ruelle and Quantum Resonances for Open Hyperbolic Manifolds

TL;DR

This paper establishes a direct link between classical geodesic flow spectra and quantum Laplacian spectra on open hyperbolic manifolds, extending previous results from cocompact to convex cocompact cases.

Contribution

It extends the classical-quantum correspondence to convex cocompact hyperbolic manifolds, broadening the understanding of spectral relationships in non-compact settings.

Findings

Classical and quantum spectra are directly related on convex cocompact hyperbolic manifolds.

The work generalizes previous results from cocompact to convex cocompact cases.

Provides new insights into the spectral theory of hyperbolic manifolds.

Abstract

We establish a direct classical-quantum correspondence on convex cocompact hyperbolic manifolds between the spectrums of the geodesic flow and the Laplacian acting on natural tensor bundles. This extends previous work detailing the correspondence for cocompact quotients.