A Transformational Property of the Husimi Function and Its Relation to the Wigner Function and Symplectic Tomograms
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Аутори
Andreev, V. A.Davidović, Dragomir M.
Davidović, Ljubica D.
Davidović, Milena D.
Man'ko, V. I.
Man'ko, M. A.
Чланак у часопису
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Приказ свих података о документуАпстракт
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) - GT (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.
Кључне речи:
quantum mechanics / Husimi function / Wigner function / symplectic tomogram / scale transformationИзвор:
Theoretical and Mathematical Physics, 2011, 166, 3, 356-368Финансирање / пројекти:
- Russian Foundation for Basic Research [08-02-00741, 09-02-00142, 10-02-00312], Serbian Ministry of Science and Technological Development
DOI: 10.1007/s11232-011-0028-8
ISSN: 0040-5779; 1573-9333
WoS: 000293733500006
Scopus: 2-s2.0-79955090743
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Институција/група
VinčaTY - JOUR AU - Andreev, V. A. AU - Davidović, Dragomir M. AU - Davidović, Ljubica D. AU - Davidović, Milena D. AU - Man'ko, V. I. AU - Man'ko, M. A. PY - 2011 UR - https://vinar.vin.bg.ac.rs/handle/123456789/4443 AB - 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) - GT (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. T2 - Theoretical and Mathematical Physics T1 - A Transformational Property of the Husimi Function and Its Relation to the Wigner Function and Symplectic Tomograms VL - 166 IS - 3 SP - 356 EP - 368 DO - 10.1007/s11232-011-0028-8 ER -
@article{ author = "Andreev, V. A. and Davidović, Dragomir M. and Davidović, Ljubica D. and Davidović, Milena D. and Man'ko, V. I. and Man'ko, M. A.", year = "2011", 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) - GT (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.", journal = "Theoretical and Mathematical Physics", title = "A Transformational Property of the Husimi Function and Its Relation to the Wigner Function and Symplectic Tomograms", volume = "166", number = "3", pages = "356-368", doi = "10.1007/s11232-011-0028-8" }
Andreev, V. A., Davidović, D. M., Davidović, L. D., Davidović, M. D., Man'ko, V. I.,& Man'ko, M. A.. (2011). A Transformational Property of the Husimi Function and Its Relation to the Wigner Function and Symplectic Tomograms. in Theoretical and Mathematical Physics, 166(3), 356-368. https://doi.org/10.1007/s11232-011-0028-8
Andreev VA, Davidović DM, Davidović LD, Davidović MD, Man'ko VI, Man'ko MA. A Transformational Property of the Husimi Function and Its Relation to the Wigner Function and Symplectic Tomograms. in Theoretical and Mathematical Physics. 2011;166(3):356-368. doi:10.1007/s11232-011-0028-8 .
Andreev, V. A., Davidović, Dragomir M., Davidović, Ljubica D., Davidović, Milena D., Man'ko, V. I., Man'ko, M. A., "A Transformational Property of the Husimi Function and Its Relation to the Wigner Function and Symplectic Tomograms" in Theoretical and Mathematical Physics, 166, no. 3 (2011):356-368, https://doi.org/10.1007/s11232-011-0028-8 . .