Generic Jumps of Fredholm Indices and the Quantum Hall Effect
Joseph E. Avron, Lorenzo Sadun
TL;DR
This paper explores the typical behavior of Fredholm indices in Toeplitz operators and connects these mathematical properties to open questions in the Quantum Hall Effect.
Contribution
It introduces a general analysis of Fredholm indices in Toeplitz operators and links these findings to conjectures in quantum physics.
Findings
Fredholm indices exhibit generic behavior in Toeplitz operators
Connections established between mathematical indices and Quantum Hall Effect conjectures
Provides insights into open problems in quantum physics
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.
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Taxonomy
TopicsQuantum and electron transport phenomena · Spectral Theory in Mathematical Physics · Graphene research and applications