Arithmetic unique ergodicity for infinite dimensional flat bundles

TL;DR

This paper establishes a uniform quantum unique ergodicity result for high-frequency eigensections in infinite-dimensional flat bundles over arithmetic surfaces, advancing understanding of quantum chaos in complex geometric settings.

Contribution

It introduces a uniform ergodicity theorem for high-frequency eigensections in infinite-dimensional flat bundles, a novel extension in quantum ergodicity theory.

Findings

Proves uniform quantum unique ergodicity for specific flat bundles

Demonstrates ergodic behavior of high-frequency eigensections

Extends quantum ergodicity results to infinite-dimensional settings

Abstract

In this paper, we prove a uniform version of quantum unique ergodicity for high-frequency eigensections of a certain series of unitary flat bundles over arithmetic surfaces.