Spectral Properties and the Behavior of the Current-Current Correlation Measure for the Luttinger-Sy Model

Author

• Jonathan Benoit, University of KentuckyFollow

Date Available

7-8-2026

Year of Publication

2026

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

Arts and Sciences

Department/School/Program

Mathematics

Faculty

Peter Hislop

Faculty

Bert Guillou

Abstract

The Luttinger-Sy Model, sometimes referred to as the Pieces Model, is a Random Schrodinger Operator on L²(R) which is characterized in part by "pieces" whose endpoints are chosen by a Poisson Point Process. The Hamiltonian in this setting is then given as a direct sum of Laplacians with Dirchlet boundary conditions on each piece. In this work, we show several spectral properties of the Luttinger-Sy Model, including proving the deterministic spectrum is [0,infinity) and that a Wegner-type and Minami-type estimate both hold. Additionally, we show that the finite-volume Current-Current Correlation Measure is singular continuous with respect the Lebesgue measure.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2026.344

Archival?

Archival

Recommended Citation

Benoit, Jonathan, "Spectral Properties and the Behavior of the Current-Current Correlation Measure for the Luttinger-Sy Model" (2026). Theses and Dissertations--Mathematics. 133.
https://uknowledge.uky.edu/math_etds/133