Topological quantization of ensemble averages
نویسنده
چکیده
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 [1] 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. Topological quantization of ensemble averages 2
منابع مشابه
Non-commutative calculus and topological quantization of ensemble averages in quantum mechanics
We define the current of a quantum observable and connect its ensemble average to the index of an operator. The formalism is applied to the quantization of electrical conductance in atomic wires.
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