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Scaling Transform and Stretched States in Quantum Mechanics

Authorized Users Only
2016
Authors
Andreev, Vladimir A.
Davidović, Dragomir M.
Davidović, Ljubica D.
Davidović, Milos D.
Davidović, Milena
Zotov, Sergey D.
Article (Published version)
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Abstract
We consider the Husimi Q(q, p)-functions which are quantum quasiprobability distributions on the phase space. It is known that, under a scaling transform (q; p) - gt (aiiq; aiip), the Husimi function of any physical state is converted into a function which is also the Husimi function of some physical state. More precisely, it has been proved that, if Q(q, p) is the Husimi function, the function aii(2) Q(aiiq; aiip) is also the Husimi function. We call a state with the Husimi function aii(2) Q(aiiq; aiip) the stretched state and investigate the properties of the stretched Fock states. These states can be obtained as a result of applying the scaling transform to the Fock states of the harmonic oscillator. The harmonic-oscillator Fock states are pure states, but the stretched Fock states are mixed states. We find the density matrices of stretched Fock states in an explicit form. Their structure can be described with the help of negative binomial distributions. We present the graphs of dis...tributions of negative binomial coefficients for different stretched Fock states and show the von Neumann entropy of the simplest stretched Fock state.

Keywords:
Husimi function / harmonic oscillator / scaling transform / Fock states / stretched states
Source:
Journal of Russian Laser Research, 2016, 37, 5, 434-439
Publisher:
  • Springer New York LLC
Funding / projects:
  • Physical Implications of Modified Spacetime (RS-171031)
  • A new approach to foundational problems of quantum mechanics related to applications in quantum technologies and interpretations of signals of various origins (RS-171028)
  • Russian Foundation for Basic Research 14-08-00981_a

DOI: 10.1007/s10946-016-9594-4

ISSN: 1071-2836

WoS: 000388183000004

Scopus: 2-s2.0-84994418090
[ Google Scholar ]
2
1
URI
https://grafar.grf.bg.ac.rs/handle/123456789/807
Collections
  • Radovi istraživača / Researcher's publications
  • Катедра за математику, физику и нацртну геометрију
Institution/Community
GraFar
TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Dragomir M.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milos D.
AU  - Davidović, Milena
AU  - Zotov, Sergey D.
PY  - 2016
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/807
AB  - We consider the Husimi Q(q, p)-functions which are quantum quasiprobability distributions on the phase space. It is known that, under a scaling transform (q; p) - gt (aiiq; aiip), the Husimi function of any physical state is converted into a function which is also the Husimi function of some physical state. More precisely, it has been proved that, if Q(q, p) is the Husimi function, the function aii(2) Q(aiiq; aiip) is also the Husimi function. We call a state with the Husimi function aii(2) Q(aiiq; aiip) the stretched state and investigate the properties of the stretched Fock states. These states can be obtained as a result of applying the scaling transform to the Fock states of the harmonic oscillator. The harmonic-oscillator Fock states are pure states, but the stretched Fock states are mixed states. We find the density matrices of stretched Fock states in an explicit form. Their structure can be described with the help of negative binomial distributions. We present the graphs of distributions of negative binomial coefficients for different stretched Fock states and show the von Neumann entropy of the simplest stretched Fock state.
PB  - Springer New York LLC
T2  - Journal of Russian Laser Research
T1  - Scaling Transform and Stretched States in Quantum Mechanics
EP  - 439
IS  - 5
SP  - 434
VL  - 37
DO  - 10.1007/s10946-016-9594-4
ER  - 
@article{
author = "Andreev, Vladimir A. and Davidović, Dragomir M. and Davidović, Ljubica D. and Davidović, Milos D. and Davidović, Milena and Zotov, Sergey D.",
year = "2016",
abstract = "We consider the Husimi Q(q, p)-functions which are quantum quasiprobability distributions on the phase space. It is known that, under a scaling transform (q; p) - gt (aiiq; aiip), the Husimi function of any physical state is converted into a function which is also the Husimi function of some physical state. More precisely, it has been proved that, if Q(q, p) is the Husimi function, the function aii(2) Q(aiiq; aiip) is also the Husimi function. We call a state with the Husimi function aii(2) Q(aiiq; aiip) the stretched state and investigate the properties of the stretched Fock states. These states can be obtained as a result of applying the scaling transform to the Fock states of the harmonic oscillator. The harmonic-oscillator Fock states are pure states, but the stretched Fock states are mixed states. We find the density matrices of stretched Fock states in an explicit form. Their structure can be described with the help of negative binomial distributions. We present the graphs of distributions of negative binomial coefficients for different stretched Fock states and show the von Neumann entropy of the simplest stretched Fock state.",
publisher = "Springer New York LLC",
journal = "Journal of Russian Laser Research",
title = "Scaling Transform and Stretched States in Quantum Mechanics",
pages = "439-434",
number = "5",
volume = "37",
doi = "10.1007/s10946-016-9594-4"
}
Andreev, V. A., Davidović, D. M., Davidović, L. D., Davidović, M. D., Davidović, M.,& Zotov, S. D.. (2016). Scaling Transform and Stretched States in Quantum Mechanics. in Journal of Russian Laser Research
Springer New York LLC., 37(5), 434-439.
https://doi.org/10.1007/s10946-016-9594-4
Andreev VA, Davidović DM, Davidović LD, Davidović MD, Davidović M, Zotov SD. Scaling Transform and Stretched States in Quantum Mechanics. in Journal of Russian Laser Research. 2016;37(5):434-439.
doi:10.1007/s10946-016-9594-4 .
Andreev, Vladimir A., Davidović, Dragomir M., Davidović, Ljubica D., Davidović, Milos D., Davidović, Milena, Zotov, Sergey D., "Scaling Transform and Stretched States in Quantum Mechanics" in Journal of Russian Laser Research, 37, no. 5 (2016):434-439,
https://doi.org/10.1007/s10946-016-9594-4 . .

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