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.
Keywords:
quantum mechanics / Husimi function / Wigner function / symplectic tomogram / scale transformation
Source:
Theoretical and Mathematical Physics, 2011, 166, 3, 356-368
Funding / projects:
Russian Foundation for Basic Research 08-02-00741
Russian Foundation for Basic Research 09-02-00142
Russian Foundation for Basic Research 10-02-00312
Serbian Ministry of Science and Technological Development
TY - JOUR
AU - Andreev, Vladimir A.
AU - Davidović, Dragomir M.
AU - Davidović, Ljubica D.
AU - Davidović, Milena
AU - Man'ko, V. I.
AU - Manko, M. A.
PY - 2011
UR - https://grafar.grf.bg.ac.rs/handle/123456789/351
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
EP - 368
IS - 3
SP - 356
VL - 166
DO - 10.1007/s11232-011-0028-8
ER -
@article{
author = "Andreev, Vladimir A. and Davidović, Dragomir M. and Davidović, Ljubica D. and Davidović, Milena and Man'ko, V. I. and Manko, 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",
pages = "368-356",
number = "3",
volume = "166",
doi = "10.1007/s11232-011-0028-8"
}
Andreev, V. A., Davidović, D. M., Davidović, L. D., Davidović, M., Man'ko, V. I.,& Manko, 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 M, Man'ko VI, Manko 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, Vladimir A., Davidović, Dragomir M., Davidović, Ljubica D., Davidović, Milena, Man'ko, V. I., Manko, 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 . .
