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Equality of bulk and edge Hall conductance revisited

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P. Elbau, G.M. Graf

Mathematical Physics · Submitted 11 Mar 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The equality of conductances is an expression of the stability of that index as a flux tube is moved from within the bulk across the boundary of a sample.

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arXiv IDmath-ph/0203019 (version 1)
Pith IDRR6YWXBV, Pith's permanent record of this paper and its review
CitationG.M. Graf, P. Elbau. "Equality of bulk and edge Hall conductance revisited." arXiv:math-ph/0203019 (2002). https://pith.science/paper/RR6YWXBV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,603 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.89 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The integral quantum Hall effect can be explained either as resulting from bulk or edge currents (or, as it occurs in real samples, as a combination of both). This leads to different definitions of Hall conductance, which agree under appropriate hypotheses, as shown by Schulz-Baldes et al. by means of K-theory. We propose an alternative proof based on a generalization of the index of a pair of projections to more general operators. The equality of conductances is an expression of the stability of that index as a flux tube is moved from within the bulk across the boundary of a sample.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The integral quantum Hall effect can be explained either as resulting from bulk or edge currents (or, as it occurs in real samples, as a combination of both). background 1.00 0.05 0.04 asserted 0.75
s1 This leads to different definitions of Hall conductance, which agree under appropriate hypotheses, as shown by Schulz-Baldes et al. by means of K-theory. background 1.00 0.04 0.11 asserted 1.00
s2 We propose an alternative proof based on a generalization of the index of a pair of projections to more general operators. contribution 0.85 0.92 0.11 asserted 0.93
s3 The equality of conductances is an expression of the stability of that index as a flux tube is moved from within the bulk across the boundary of a sample. interpretation 0.99 0.55 0.58 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The integral quantum Hall effect can be explained either as resulting from bulk or edge currents (or, as it occurs in real samples, as a combination of both). This leads to different definitions of Hall conductance, which agree under appropriate hypotheses, as shown by Schulz-Baldes et al. by means of K-theory. We propose an alternative proof based on a generalization of the index of a pair of projections to more general operators. The equality of conductances is an expression of the stability of that index as a flux tube is moved from within the bulk across the boundary of a sample.

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2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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