General information
Latest issue
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS


Personal entry:
Save password
Forgotten password?

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


Full text: PDF file (452 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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
    Number of views:
    This page:578
    Full text:145
    First page:25

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020