# Quantum ergodicity for pseudo-Laplacians

## TL;DR

This paper proves quantum ergodicity for eigenfunctions of the pseudo-Laplacian on certain Riemannian surfaces with hyperbolic cusps, linking spectral properties to classical ergodic dynamics.

## Contribution

It establishes quantum ergodicity results for pseudo-Laplacians on surfaces with hyperbolic cusps, extending understanding of eigenfunction distribution in these geometries.

## Key findings

- Eigenfunctions become uniformly distributed in the high-energy limit.
- Quantum ergodicity holds for pseudo-Laplacians on surfaces with hyperbolic cusps.
- The geodesic flow's ergodicity influences eigenfunction behavior.

## Abstract

We prove quantum ergodicity for the eigenfunctions of the pseudo-Laplacian on Riemannian surfaces with finitely many hyperbolic cusps and ergodic geodesic flow.