Proof of the Kurlberg-Rudnick Rate Conjecture
Shamgar Gurevich, Ronny Hadani
TL;DR
This paper proves the Hecke quantum unique ergodicity rate conjecture for the Berry-Hannay model, a quantum mechanics model on a 2D torus, confirming long-standing theoretical predictions.
Contribution
It provides the first rigorous proof of the conjecture for the Berry-Hannay model, advancing understanding of quantum chaos on the torus.
Findings
Proof of the Hecke quantum unique ergodicity rate conjecture
Confirmation of theoretical predictions in quantum chaos
Advancement in mathematical understanding of quantum ergodicity
Abstract
In this paper we present a proof of the {\it Hecke quantum unique ergodicity rate conjecture} for the Berry-Hannay model. A model of quantum mechanics on the 2-dimensional torus. This conjecture was stated in Z. Rudnick's lectures at MSRI, Berkeley 1999 and ECM, Barcelona 2000.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Chemical Thermodynamics and Molecular Structure · Geometry and complex manifolds