Quantum Measurement in Electric Circuit

L. S. Levitov; G. B. Lesovik

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arXiv · cond-mat/9401004

Quantum Measurement in Electric Circuit

L. S. Levitov·G. B. Lesovik

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Abstract

We study fluctuations of electric current in a quantum resistor and derive a general quantum-mechanical formula for the distribution of transmitted charge. For that we introduce a scheme of current measurement that involves a spin $1/2$ coupled to the current so that it precesses at the rate proportional to the current. Our approach allows the study of charge transfer without breaking the circuit. We analyze a single channel conductor and derive electron counting statistics for arbitrary relation between temperature and voltage. For a perfectly transmitting channel the counting distribution is gaussian, both for zero-point fluctuations and at finite temperature. At constant voltage and low temperature the distribution is binomial, i.e., it arises from Bernoulli statistics.

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L. S. Levitov, G. B. Lesovik. 1994-01-03. Quantum Measurement in Electric Circuit. https://arxiv.org/abs/cond-mat/9401004

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