A Wegner estimate for multi-particle random Hamiltonians
Werner Kirsch
TL;DR
This paper establishes a Wegner estimate for multi-particle Anderson Hamiltonians on the lattice, which is a key step towards proving Anderson localization in such complex quantum systems.
Contribution
It introduces a Wegner estimate applicable to a broad class of multi-particle Hamiltonians, advancing the mathematical understanding of localization phenomena.
Findings
Wegner estimate proven for multi-particle systems
Foundation laid for proving Anderson localization in these systems
Enhances mathematical tools for analyzing quantum disordered systems
Abstract
We prove a Wegner estimate for a large class of multiparticle Anderson Hamiltonians on the lattice. These estimates will allow us to prove Anderson localization for such systems. A detailed proof of localization will be given in a subsequent paper.
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
TopicsSpectral Theory in Mathematical Physics · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems