Topological quantization of ensemble averages

Details Topological quantization of ensemble averages Topological quantization of ensemble averages

2008-03-22

arxiv.org/abs/0803.3274v3

J. Phys. A: Math. Theor. 42, 065207 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

16 pages, 2 figures

Scientific paper

10.1088/1751-8113/42/6/065207

We define the current of a quantum observable and, under well defined conditions, we connect its ensemble average to the index of a Fredholm operator. The present work builds on a formalism developed by Kellendonk and Schulz-Baldes \cite{Kellendonk:2004p597} to study the quantization of edge currents for continuous magnetic Schroedinger operators. The generalization given here may be a useful tool to scientists looking for novel manifestations of the topological quantization. As a new application, we show that the differential conductance of atomic wires is given by the index of a certain operator. We also comment on how the formalism can be used to probe the existence of edge states.

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