On a conjecture by Hundertmark and Simon

The main result of this paper is a complete proof of a new Lieb–Thirring-type inequality for Jacobi matrices originally conjectured by Hundertmark and Simon. In particular, it is proved that the estimate on the sum of eigenvalues does not depend on the off-diagonal terms as long as they are smaller...

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Bibliographic Details
Main Authors: Ari Laptev, Michael Loss, Lukas Schimmer
Format: Article in Journal/Newspaper
Language:unknown
Published: 2022
Subjects:
Mathematical physics
Physical sciences
Nuclear and plasma physics
Particle and high energy physics
Science & Technology
Physics
Multidisciplinary
Particles & Fields
Mathematical
laptev
Online Access:https://figshare.com/articles/journal_contribution/On_a_conjecture_by_Hundertmark_and_Simon/24591981
Description
Summary:The main result of this paper is a complete proof of a new Lieb–Thirring-type inequality for Jacobi matrices originally conjectured by Hundertmark and Simon. In particular, it is proved that the estimate on the sum of eigenvalues does not depend on the off-diagonal terms as long as they are smaller than their asymptotic value. An interesting feature of the proof is that it employs a technique originally used by Hundertmark–Laptev–Weidl concerning sums of singular values for compact operators. This technique seems to be novel in the context of Jacobi matrices.

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