TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Dragomir M.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milos D.
AU  - Davidović, Milena
PY  - 2017
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/877
AB  - We consider scale transformations (q, p) - gt (lambda q, lambda p) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson-Schrodinger uncertainty relations for stretched states.
PB  - Maik Nauka Publishing / Springer SBM
T2  - Theoretical and Mathematical Physics
T1  - Scale transformations in phase space and stretched states of a harmonic oscillator
EP  - 1096
IS  - 1
SP  - 1080
VL  - 192
DO  - 10.1134/S0040577917070091
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Dragomir M. and Davidović, Ljubica D. and Davidović, Milos D. and Davidović, Milena",
year = "2017",
abstract = "We consider scale transformations (q, p) - gt (lambda q, lambda p) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson-Schrodinger uncertainty relations for stretched states.",
publisher = "Maik Nauka Publishing / Springer SBM",
journal = "Theoretical and Mathematical Physics",
title = "Scale transformations in phase space and stretched states of a harmonic oscillator",
pages = "1096-1080",
number = "1",
volume = "192",
doi = "10.1134/S0040577917070091"
}

Andreev, V. A., Davidović, D. M., Davidović, L. D., Davidović, M. D.,& Davidović, M.. (2017). Scale transformations in phase space and stretched states of a harmonic oscillator. in Theoretical and Mathematical Physics
Maik Nauka Publishing / Springer SBM., 192(1), 1080-1096.
https://doi.org/10.1134/S0040577917070091

Andreev VA, Davidović DM, Davidović LD, Davidović MD, Davidović M. Scale transformations in phase space and stretched states of a harmonic oscillator. in Theoretical and Mathematical Physics. 2017;192(1):1080-1096.
doi:10.1134/S0040577917070091 .

Andreev, Vladimir A., Davidović, Dragomir M., Davidović, Ljubica D., Davidović, Milos D., Davidović, Milena, "Scale transformations in phase space and stretched states of a harmonic oscillator" in Theoretical and Mathematical Physics, 192, no. 1 (2017):1080-1096,
https://doi.org/10.1134/S0040577917070091 . .

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 . .

TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Milena
AU  - Davidović, Ljubica D.
AU  - Davidović, Milos D.
AU  - Davidović, Dragomir M.
PY  - 2015
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/666
AB  - We propose a new method for the derivation of Husimi symbols, for operators that are given in the form of products of an arbitrary number of coordinates, and momentum operators, in an arbitrary order. For such an operator, in the standard approach, one expresses coordinate and momentum operators as a linear combination of the creation and annihilation operators, and then uses the antinormal ordering to obtain the final form of the symbol. In our method, one obtains the Husimi symbol in a much more straightforward fashion, departing directly from operator explicit form without transforming it through creation and annihilation operators. With this method the mean values of some operators are found. It is shown how the Heisenberg and the Schrodinger-Robertson uncertainty relations, for position and momentum, are transformed under scale transformation (q; p) - gt (lambda q; lambda p). The physical sense of some states which can be constructed with this transformation is also discussed.
PB  - Institute of Physics Publishing
T2  - Physica Scripta
T1  - Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations
IS  - 7
VL  - 90
DO  - 10.1088/0031-8949/90/7/074023
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Milena and Davidović, Ljubica D. and Davidović, Milos D. and Davidović, Dragomir M.",
year = "2015",
abstract = "We propose a new method for the derivation of Husimi symbols, for operators that are given in the form of products of an arbitrary number of coordinates, and momentum operators, in an arbitrary order. For such an operator, in the standard approach, one expresses coordinate and momentum operators as a linear combination of the creation and annihilation operators, and then uses the antinormal ordering to obtain the final form of the symbol. In our method, one obtains the Husimi symbol in a much more straightforward fashion, departing directly from operator explicit form without transforming it through creation and annihilation operators. With this method the mean values of some operators are found. It is shown how the Heisenberg and the Schrodinger-Robertson uncertainty relations, for position and momentum, are transformed under scale transformation (q; p) - gt (lambda q; lambda p). The physical sense of some states which can be constructed with this transformation is also discussed.",
publisher = "Institute of Physics Publishing",
journal = "Physica Scripta",
title = "Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations",
number = "7",
volume = "90",
doi = "10.1088/0031-8949/90/7/074023"
}

Andreev, V. A., Davidović, M., Davidović, L. D., Davidović, M. D.,& Davidović, D. M.. (2015). Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations. in Physica Scripta
Institute of Physics Publishing., 90(7).
https://doi.org/10.1088/0031-8949/90/7/074023

Andreev VA, Davidović M, Davidović LD, Davidović MD, Davidović DM. Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations. in Physica Scripta. 2015;90(7).
doi:10.1088/0031-8949/90/7/074023 .

Andreev, Vladimir A., Davidović, Milena, Davidović, Ljubica D., Davidović, Milos D., Davidović, Dragomir M., "Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations" in Physica Scripta, 90, no. 7 (2015),
https://doi.org/10.1088/0031-8949/90/7/074023 . .

TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milena
AU  - Davidović, Milos D.
AU  - Man'ko, V. I.
AU  - Manko, M. A.
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/645
AB  - We propose a new method for calculating Husimi symbols of operators. In contrast to the standard method, it does not require using the anti-normal-ordering procedure. According to this method, the coordinate and momentum operators (q) over cap and (p) over cap are assigned other operators (X) over cap and (P) over cap satisfying the same commutation relations. We then find the result of acting with the (X) over cap and (P) over cap operators and also polynomials in these operators on the Husimi function. After the obtained expression is integrated over the phase space coordinates, the integrand becomes a Husimi function times the symbol of the operator chosen to act on that function. We explicitly evaluate the Husimi symbols for operators that are powers of (X) over cap or (P) over cap.
PB  - Maik Nauka Publishing / Springer SBM
T2  - Theoretical and Mathematical Physics
T1  - Operator method for calculating q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols
EP  - 573
IS  - 2
SP  - 559
VL  - 179
DO  - 10.1007/s11232-014-0162-1
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Ljubica D. and Davidović, Milena and Davidović, Milos D. and Man'ko, V. I. and Manko, M. A.",
year = "2014",
abstract = "We propose a new method for calculating Husimi symbols of operators. In contrast to the standard method, it does not require using the anti-normal-ordering procedure. According to this method, the coordinate and momentum operators (q) over cap and (p) over cap are assigned other operators (X) over cap and (P) over cap satisfying the same commutation relations. We then find the result of acting with the (X) over cap and (P) over cap operators and also polynomials in these operators on the Husimi function. After the obtained expression is integrated over the phase space coordinates, the integrand becomes a Husimi function times the symbol of the operator chosen to act on that function. We explicitly evaluate the Husimi symbols for operators that are powers of (X) over cap or (P) over cap.",
publisher = "Maik Nauka Publishing / Springer SBM",
journal = "Theoretical and Mathematical Physics",
title = "Operator method for calculating q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols",
pages = "573-559",
number = "2",
volume = "179",
doi = "10.1007/s11232-014-0162-1"
}

Andreev, V. A., Davidović, L. D., Davidović, M., Davidović, M. D., Man'ko, V. I.,& Manko, M. A.. (2014). Operator method for calculating q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols. in Theoretical and Mathematical Physics
Maik Nauka Publishing / Springer SBM., 179(2), 559-573.
https://doi.org/10.1007/s11232-014-0162-1

Andreev VA, Davidović LD, Davidović M, Davidović MD, Man'ko VI, Manko MA. Operator method for calculating q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols. in Theoretical and Mathematical Physics. 2014;179(2):559-573.
doi:10.1007/s11232-014-0162-1 .

Andreev, Vladimir A., Davidović, Ljubica D., Davidović, Milena, Davidović, Milos D., Man'ko, V. I., Manko, M. A., "Operator method for calculating q symbols and their relation to weyl-wigner symbols and symplectic tomogram symbols" in Theoretical and Mathematical Physics, 179, no. 2 (2014):559-573,
https://doi.org/10.1007/s11232-014-0162-1 . .

TY  - CONF
AU  - Božić, Mirjana
AU  - Davidović, Milena
AU  - Kapor, Agnes
AU  - Knežević, D.
AU  - Pavkov-Hrvojević, M.
AU  - Puač, N.
AU  - Savić, Ilija
AU  - Stojanović, M.
AU  - Marković-Topalović, Tatjana
PY  - 2013
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/551
AB  - The trend of the increasing participation and importance of female physicists in Serbia continues. Many women have taken leading position in research and faculty governance and are contributing significantly to educational reform and the improvement of physics education in the primary and secondary schools.
C3  - AIP Conference Proceedings
T1  - The impact of educational reform and categorization of scientific journals and scientists on physics in Serbia
EP  - 147
SP  - 146
VL  - 1517
DO  - 10.1063/1.4794262
ER  - 

@conference{
author = "Božić, Mirjana and Davidović, Milena and Kapor, Agnes and Knežević, D. and Pavkov-Hrvojević, M. and Puač, N. and Savić, Ilija and Stojanović, M. and Marković-Topalović, Tatjana",
year = "2013",
abstract = "The trend of the increasing participation and importance of female physicists in Serbia continues. Many women have taken leading position in research and faculty governance and are contributing significantly to educational reform and the improvement of physics education in the primary and secondary schools.",
journal = "AIP Conference Proceedings",
title = "The impact of educational reform and categorization of scientific journals and scientists on physics in Serbia",
pages = "147-146",
volume = "1517",
doi = "10.1063/1.4794262"
}

Božić, M., Davidović, M., Kapor, A., Knežević, D., Pavkov-Hrvojević, M., Puač, N., Savić, I., Stojanović, M.,& Marković-Topalović, T.. (2013). The impact of educational reform and categorization of scientific journals and scientists on physics in Serbia. in AIP Conference Proceedings, 1517, 146-147.
https://doi.org/10.1063/1.4794262

Božić M, Davidović M, Kapor A, Knežević D, Pavkov-Hrvojević M, Puač N, Savić I, Stojanović M, Marković-Topalović T. The impact of educational reform and categorization of scientific journals and scientists on physics in Serbia. in AIP Conference Proceedings. 2013;1517:146-147.
doi:10.1063/1.4794262 .

Božić, Mirjana, Davidović, Milena, Kapor, Agnes, Knežević, D., Pavkov-Hrvojević, M., Puač, N., Savić, Ilija, Stojanović, M., Marković-Topalović, Tatjana, "The impact of educational reform and categorization of scientific journals and scientists on physics in Serbia" in AIP Conference Proceedings, 1517 (2013):146-147,
https://doi.org/10.1063/1.4794262 . .