Publication Date:
2011-04-24
Description:
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) → (λq, λp). 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. Content Type Journal Article Pages 356-368 DOI 10.1007/s11232-011-0028-8 Authors V. A. Andreev, Lebedev Physical Institute, RAS, Moscow, Russia D. M. Davidović, Vinca Institute of Nuclear Sciences, Belgrade, Serbia L. D. Davidović, Institute of Physics, Belgrade, Serbia M. D. Davidović, Faculty of Civil Engineering, Belgrade University, Belgrade, Serbia V. I. Man’ko, Lebedev Physical Institute, RAS, Moscow, Russia M. A. Man’ko, Lebedev Physical Institute, RAS, Moscow, Russia Journal Theoretical and Mathematical Physics Online ISSN 1573-9333 Print ISSN 0040-5779 Journal Volume Volume 166 Journal Issue Volume 166, Number 3
Print ISSN:
0040-5779
Topics:
Mathematics
,
Physics
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