2002/03/11 by P. Elbau, G. M. Graf · 3 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Boundary (topology) #Conductance #Enhanced Data Rates for GSM Evolution #Flux tube #Generalization #Hall effect #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Stability (learning theory) #Surface and Thin Film Phenomena #math-ph #math.MP #msc:81Q10 #msc:81V70
paper · pdf · doi:10.1007/s00220-002-0698-z
LaTeX with 1 .pstex/.pstex_t figure
arxiv created 2002/03/11 · openalex publication_date 2002/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.