Generic Jumps of Fredholm Indices and the Quantum Hall Effect

2000/03/05 by J. E. Avron, Joseph E. Avron, Lorenzo Sadun +2
Materials Science · Mathematics · Physics and Astronomy · #46C05 #81Q70 #81V70 #FOS: Physical sciences #Graphene research and applications #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum and electron transport phenomena #Spectral Theory in Mathematical Physics #cond-mat.mes-hall #math-ph #math.MP #msc:46C05 #msc:81Q70 #msc:81V70

paper · pdf · doi:10.48550/arxiv.math-ph/0003003

LateX, 17 pages, including one embedded postscript figure

arxiv created 2000/03/05 · openalex publication_date 2000/03/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the generic behavior of Fredholm indices in the space of Toeplitz operators. We relate this behavior to certain conjectures and open problems that arise in the context of the Quantum Hall Effect.

Related

• Fock space: A bridge between Fredholm index and the quantum Hall effect
• The Bott index of two unitary operators and the integer quantum Hall effect
• Topological quantum numbers in the Hall effect
• Wave Functions Statistics at Quantum Hall Critical Point
• New Classical Limits of Quantum Theories