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TMF, 2011, Volume 166, Number 3, Pages 410–424 (Mi tmf6619)  

This article is cited in 8 scientific papers (total in 8 papers)

A transformational property of the Husimi function and its relation to the Wigner function and symplectic tomograms

V. A. Andreeva, D. M. Davidovichb, L. D. Davidovichc, M. D. Davidovichd, V. I. Man'koa, M. A. Man'koa

a Lebedev Physical Institute, RAS, Moscow, Russia
b Institute of Nuclear Sciences Vinca, Belgrade, Serbia
c Institute of Physics, Belgrade, Serbia
d Faculty of Civil Engineering, Belgrade University, Belgrade, Serbia

Abstract: We consider the Husimi $Q$-functions, which are quantum quasiprobability distributions in the phase space, and investigate their transformation properties under a scale transformation $(q,p)\to(\lambda q,\lambda p)$. We prove a theorem that under this transformation, the Husimi function of a physical state is transformed into a function that is also a Husimi function of some physical state. Therefore, the scale transformation defines a positive map of density operators. We investigate the relation of Husimi functions to Wigner functions and symplectic tomograms and establish how they transform under the scale transformation. As an example, we consider the harmonic oscillator and show how its states transform under the scale transformation.

Keywords: quantum mechanics, Husimi function, Wigner function, symplectic tomogram, scale transformation


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English version:
Theoretical and Mathematical Physics, 2011, 166:3, 356–368

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Received: 08.06.2010
Revised: 06.10.2010

Citation: V. A. Andreev, D. M. Davidovich, L. D. Davidovich, M. D. Davidovich, V. I. Man'ko, M. A. Man'ko, “A transformational property of the Husimi function and its relation to the Wigner function and symplectic tomograms”, TMF, 166:3 (2011), 410–424; Theoret. and Math. Phys., 166:3 (2011), 356–368

Citation in format AMSBIB
\by V.~A.~Andreev, D.~M.~Davidovich, L.~D.~Davidovich, M.~D.~Davidovich, V.~I.~Man'ko, M.~A.~Man'ko
\paper A~transformational property of the~Husimi function and its relation to the~Wigner function and symplectic tomograms
\jour TMF
\yr 2011
\vol 166
\issue 3
\pages 410--424
\jour Theoret. and Math. Phys.
\yr 2011
\vol 166
\issue 3
\pages 356--368

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    This publication is cited in the following articles:
    1. Filippov S.N., Man'ko V.I., “Measuring microwave quantum states: Tomogram and moments”, Phys Rev A, 84:3 (2011), 033827  crossref  adsnasa  isi  elib  scopus
    2. V. A. Andreev, L. D. Davidovich, Milena D. Davidovich, Miloš D. Davidovic, V. I. Man'ko, M. A. Man'ko, “Operator method for calculating $Q$ symbols and their relation to Weyl–Wigner symbols and symplectic tomogram symbols”, Theoret. and Math. Phys., 179:2 (2014), 559–573  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. P. Adam, V. A. Andreev, A. Isar, V. I. Man'ko, M. A. Man'ko, “Star product, discrete Wigner functions, and spin-system tomograms”, Theoret. and Math. Phys., 186:3 (2016), 346–364  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. Adam P. Andreev V.A. Isar A. Man'ko M.A. Man'ko V.I., “Continuous Sets of Dequantizers and Quantizers for One-Qubit States*”, J. Russ. Laser Res., 37:6 (2016), 544–555  crossref  isi  scopus
    5. Andreev V.A. Davidovic D.M. Davidovic L.D. Davidovic M.D. Davidovic M.D. Zotov S.D., “Scaling Transform and Stretched States in Quantum Mechanics”, J. Russ. Laser Res., 37:5 (2016), 434–439  crossref  isi  scopus
    6. V. A. Andreev, D. M. Davidović, L. D. Davidović, Milena D. Davidović, Miloš D. Davidović, “Scale transformations in phase space and stretched states of a harmonic oscillator”, Theoret. and Math. Phys., 192:1 (2017), 1080–1096  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. Trushechkin A., “Semiclassical Evolution of Quantum Wave Packets on the Torus Beyond the Ehrenfest Time in Terms of Husimi Distributions”, J. Math. Phys., 58:6 (2017), 062102  crossref  mathscinet  zmath  isi  scopus
    8. Adam P. Andreev V.A. Isar A. Man'ko M.A. Man'ko V.I., “Minimal Sets of Dequantizers and Quantizers For Finite-Dimensional Quantum Systems”, Phys. Lett. A, 381:34 (2017), 2778–2782  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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