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Full Counting Statistics of Non-Commuting Variables: the Case of Spin Counts

Antonio Di Lorenzo·Gabriele Campagnano·Yuli V. Nazarov
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Abstract

We discuss the Full Counting Statistics of non-commuting variables with the measurement of successive spin counts in non-collinear directions taken as an example. We show that owing to an irreducible detector back-action, the FCS in this case may be sensitive to the dynamics of the detectors, and may differ from the predictions obtained with using a naive version of the Projection Postulate. We present here a general model of detector dynamics and path-integral approach to the evaluation of FCS. We concentrate further on a simple "diffusive" model of the detector dynamics where the FCS can be evaluated with transfer-matrix method. The resulting probability distribution of spin counts is characterized by anomalously large higher cumulants and substantially deviates from Gaussian Statistics.

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Antonio Di Lorenzo, Gabriele Campagnano, Yuli V. Nazarov. 2005-10-08. Full Counting Statistics of Non-Commuting Variables: the Case of Spin Counts. https://doi.org/10.1103/physrevb.73.125311

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