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

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

2005-10-08

arxiv.org/abs/cond-mat/0510215v1

Phys. Rev. B 73, 125311 (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

11 pages, 3 figures

Scientific paper

10.1103/PhysRevB.73.125311

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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