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Full counting statistics of a general quantum mechanical variable

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Abstract.

We present a quantum mechanical framework for defining the statistics of measurements of \(\int dt \hat{A}(t)\), A(t) being a quantum mechanical variable. This is a generalization of the so-called full counting statistics proposed earlier for DC electric currents. We develop an influence functional formalism that allows us to study the quantum system along with the measuring device while fully accounting for the back action of the detector on the system to be measured. We define the full counting statistics of an arbitrary variable by means of an evolution operator that relates the initial and final density matrices of the measuring device. In this way we are able to resolve inconsistencies that occur in earlier definitions. We suggest two schemes to observe the so defined statistics experimentally.

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Authors and Affiliations

  1. Department of Applied Physics and Delft Institute of Microelectronics and Submicrontechnology, Delft University of Technology, Lorentzweg 1, 2628, CJ Delft, The Netherlands

    Yu V. Nazarov

  2. Instituut-Lorentz, Universiteit Leiden, PO Box 9506, 2300, RA Leiden, The Netherlands

    M. Kindermann

Authors
  1. Yu V. Nazarov
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  2. M. Kindermann
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Corresponding author

Correspondence to M. Kindermann.

Additional information

Received: 30 June 2003, Published online: 15 October 2003

PACS:

73.50.Td Noise processes and phenomena - 73.23.-b Electronic transport in mesoscopic systems - 74.40.+k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.)

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Nazarov, Y.V., Kindermann, M. Full counting statistics of a general quantum mechanical variable. Eur. Phys. J. B 35, 413–420 (2003). https://doi.org/10.1140/epjb/e2003-00293-1

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  • DOI: https://doi.org/10.1140/epjb/e2003-00293-1

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