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Uncertainty relation for multidimensional correlation functions

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Abstract

Partially coherent fields (mixed states) described by correlation functions (density matrices) are considered. The lower bound for the product of the uncertainties in the wave spatial localization and in its Fourier transform localization is obtained as a function of the space dimensionality. For the state with minimum uncertainty, it is shown that increasing the dimensionality leads to decreasing the phase volume corresponding to one mode in the canonical distribution of the correlation function as compared with the phase volume in the case of a coherent field (pure state).

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Authors and Affiliations

  1. Physics Institute, National Academy of Sciences of Belarus, Minsk, Belarus

    N. V. Karelin & A. M. Lazaruk

Authors
  1. N. V. Karelin
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  2. A. M. Lazaruk
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 3, pp. 427–434, December, 1998.

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Karelin, N.V., Lazaruk, A.M. Uncertainty relation for multidimensional correlation functions. Theor Math Phys 117, 1447–1452 (1998). https://doi.org/10.1007/BF02557183

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  • DOI: https://doi.org/10.1007/BF02557183

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