TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Milena D.
AU  - Davidović, Ljubica D.
AU  - Davidović, Miloš D.
AU  - Davidović, Dragomir M.
PY  - 2021
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/9164
AB  - We consider the system of N two-level atoms, of which N0 atoms are unexcited and N1 are excited. This system of N two-level atoms, which forms a linear quantum amplifier, interacts with a single-mode electromagnetic field. The problem of amplification of the L-photon states using such an amplifier is studied. The evolution of the electromagnetic field density matrix is described by the master equation for the field under amplification. The dynamics of this process is such that it can be described as the transformation of the scale of the phase space. The exact solution of the master equation is expressed using the transformed Husimi function of the L-quantum state of the harmonic oscillator. The properties of this function are studied and using it the average photon number and its fluctuations in the amplified state are found. © 2021, Editura Academiei Romane. All rights reserved.
T2  - Romanian Reports in Physics
T1  - Properties of the quantum state arising after the L-photon state has passed trough a linear quantum amplifier
VL  - 73
IS  - 1
SP  - 102
UR  - https://hdl.handle.net/21.15107/rcub_vinar_9164
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Milena D. and Davidović, Ljubica D. and Davidović, Miloš D. and Davidović, Dragomir M.",
year = "2021",
abstract = "We consider the system of N two-level atoms, of which N0 atoms are unexcited and N1 are excited. This system of N two-level atoms, which forms a linear quantum amplifier, interacts with a single-mode electromagnetic field. The problem of amplification of the L-photon states using such an amplifier is studied. The evolution of the electromagnetic field density matrix is described by the master equation for the field under amplification. The dynamics of this process is such that it can be described as the transformation of the scale of the phase space. The exact solution of the master equation is expressed using the transformed Husimi function of the L-quantum state of the harmonic oscillator. The properties of this function are studied and using it the average photon number and its fluctuations in the amplified state are found. © 2021, Editura Academiei Romane. All rights reserved.",
journal = "Romanian Reports in Physics",
title = "Properties of the quantum state arising after the L-photon state has passed trough a linear quantum amplifier",
volume = "73",
number = "1",
pages = "102",
url = "https://hdl.handle.net/21.15107/rcub_vinar_9164"
}

Andreev, V. A., Davidović, M. D., Davidović, L. D., Davidović, M. D.,& Davidović, D. M.. (2021). Properties of the quantum state arising after the L-photon state has passed trough a linear quantum amplifier. in Romanian Reports in Physics, 73(1), 102.
https://hdl.handle.net/21.15107/rcub_vinar_9164

Andreev VA, Davidović MD, Davidović LD, Davidović MD, Davidović DM. Properties of the quantum state arising after the L-photon state has passed trough a linear quantum amplifier. in Romanian Reports in Physics. 2021;73(1):102.
https://hdl.handle.net/21.15107/rcub_vinar_9164 .

Andreev, Vladimir A., Davidović, Milena D., Davidović, Ljubica D., Davidović, Miloš D., Davidović, Dragomir M., "Properties of the quantum state arising after the L-photon state has passed trough a linear quantum amplifier" in Romanian Reports in Physics, 73, no. 1 (2021):102,
https://hdl.handle.net/21.15107/rcub_vinar_9164 .

TY  - JOUR
AU  - Andreev, Vladimir A.
AU  - Davidović, Milena D.
AU  - Davidović, Ljubica D.
AU  - Davidović, Miloš D.
AU  - Davidović, Dragomir M.
PY  - 2019
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/8628
AB  - We consider a linear quantum amplifier consisting of NA two-level atoms and study the problem of amplification of N-photon states. The N-photon states are associated with N-quantum states of the harmonic oscillator. We show that the process of interaction of the electromagnetic field with atoms can be associated with some transformation of the phase space and functions defined on this phase space. We consider the Husimi functions QN(q, p) of N-quantum states of the harmonic oscillator, which are defined on the phase space, investigate transformation of these functions, and find an explicit form of the density matrix of the amplified N-photon state. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
T2  - Journal of Russian Laser Research
T1  - Linear Light Amplifier and Amplification of N-Photon States
VL  - 40
IS  - 4
SP  - 321
EP  - 327
DO  - 10.1007/s10946-019-09807-2
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Milena D. and Davidović, Ljubica D. and Davidović, Miloš D. and Davidović, Dragomir M.",
year = "2019",
abstract = "We consider a linear quantum amplifier consisting of NA two-level atoms and study the problem of amplification of N-photon states. The N-photon states are associated with N-quantum states of the harmonic oscillator. We show that the process of interaction of the electromagnetic field with atoms can be associated with some transformation of the phase space and functions defined on this phase space. We consider the Husimi functions QN(q, p) of N-quantum states of the harmonic oscillator, which are defined on the phase space, investigate transformation of these functions, and find an explicit form of the density matrix of the amplified N-photon state. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.",
journal = "Journal of Russian Laser Research",
title = "Linear Light Amplifier and Amplification of N-Photon States",
volume = "40",
number = "4",
pages = "321-327",
doi = "10.1007/s10946-019-09807-2"
}

Andreev, V. A., Davidović, M. D., Davidović, L. D., Davidović, M. D.,& Davidović, D. M.. (2019). Linear Light Amplifier and Amplification of N-Photon States. in Journal of Russian Laser Research, 40(4), 321-327.
https://doi.org/10.1007/s10946-019-09807-2

Andreev VA, Davidović MD, Davidović LD, Davidović MD, Davidović DM. Linear Light Amplifier and Amplification of N-Photon States. in Journal of Russian Laser Research. 2019;40(4):321-327.
doi:10.1007/s10946-019-09807-2 .

Andreev, Vladimir A., Davidović, Milena D., Davidović, Ljubica D., Davidović, Miloš D., Davidović, Dragomir M., "Linear Light Amplifier and Amplification of N-Photon States" in Journal of Russian Laser Research, 40, no. 4 (2019):321-327,
https://doi.org/10.1007/s10946-019-09807-2 . .

TY  - JOUR
AU  - Andreev, V. A.
AU  - Davidović, Dragomir M.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milena D.
AU  - Davidović, Miloš D.
PY  - 2017
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1685
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.
T2  - Theoretical and Mathematical Physics
T1  - Scale Transformations in Phase Space and Stretched States of a Harmonic Oscillator
VL  - 192
IS  - 1
SP  - 1080
EP  - 1096
DO  - 10.1134/S0040577917070091
ER  - 

@article{
author = "Andreev, V. A. and Davidović, Dragomir M. and Davidović, Ljubica D. and Davidović, Milena D. and Davidović, Miloš D.",
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.",
journal = "Theoretical and Mathematical Physics",
title = "Scale Transformations in Phase Space and Stretched States of a Harmonic Oscillator",
volume = "192",
number = "1",
pages = "1080-1096",
doi = "10.1134/S0040577917070091"
}

Andreev, V. A., Davidović, D. M., Davidović, L. D., Davidović, M. D.,& Davidović, M. D.. (2017). Scale Transformations in Phase Space and Stretched States of a Harmonic Oscillator. in Theoretical and Mathematical Physics, 192(1), 1080-1096.
https://doi.org/10.1134/S0040577917070091

Andreev VA, Davidović DM, Davidović LD, Davidović MD, Davidović MD. 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, V. A., Davidović, Dragomir M., Davidović, Ljubica D., Davidović, Milena D., Davidović, Miloš D., "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, Milena D.
AU  - Davidović, Miloš D.
AU  - Zotov, Sergey D.
PY  - 2016
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/1310
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.
T2  - Journal of Russian Laser Research
T1  - Scaling Transform and Stretched States in Quantum Mechanics
VL  - 37
IS  - 5
SP  - 434
EP  - 439
DO  - 10.1007/s10946-016-9594-4
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Dragomir M. and Davidović, Ljubica D. and Davidović, Milena D. and Davidović, Miloš D. 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.",
journal = "Journal of Russian Laser Research",
title = "Scaling Transform and Stretched States in Quantum Mechanics",
volume = "37",
number = "5",
pages = "434-439",
doi = "10.1007/s10946-016-9594-4"
}

Andreev, V. A., Davidović, D. M., Davidović, L. D., Davidović, M. D., Davidović, M. D.,& Zotov, S. D.. (2016). Scaling Transform and Stretched States in Quantum Mechanics. in Journal of Russian Laser Research, 37(5), 434-439.
https://doi.org/10.1007/s10946-016-9594-4

Andreev VA, Davidović DM, Davidović LD, Davidović MD, Davidović MD, 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, Milena D., Davidović, Miloš D., 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 D.
AU  - Davidovic, Ljubica D.
AU  - Davidović, Miloš D.
AU  - Davidović, Dragomir M.
PY  - 2015
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/643
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.
T2  - Physica Scripta
T1  - Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations
VL  - 90
IS  - 7
DO  - 10.1088/0031-8949/90/7/074023
ER  - 

@article{
author = "Andreev, Vladimir A. and Davidović, Milena D. and Davidovic, Ljubica D. and Davidović, Miloš 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.",
journal = "Physica Scripta",
title = "Derivation of the Husimi symbols without antinormal ordering, scale transformation and uncertainty relations",
volume = "90",
number = "7",
doi = "10.1088/0031-8949/90/7/074023"
}

Andreev, V. A., Davidović, M. D., Davidovic, 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, 90(7).
https://doi.org/10.1088/0031-8949/90/7/074023

Andreev VA, Davidović MD, Davidovic 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 D., Davidovic, Ljubica D., Davidović, Miloš 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, V. A.
AU  - Davidović, Ljubica D.
AU  - Davidović, Milena D.
AU  - Davidović, Miloš D.
AU  - Manko, V. I.
AU  - Manko, M. A.
PY  - 2014
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/6033
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.
T2  - Theoretical and Mathematical Physics
T1  - Operator Method for Calculating Q Symbols and Their Relation to Weyl-Wigner Symbols and Symplectic Tomogram Symbols
VL  - 179
IS  - 2
SP  - 559
EP  - 573
DO  - 10.1007/s11232-014-0162-1
ER  - 

@article{
author = "Andreev, V. A. and Davidović, Ljubica D. and Davidović, Milena D. and Davidović, Miloš D. and Manko, 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.",
journal = "Theoretical and Mathematical Physics",
title = "Operator Method for Calculating Q Symbols and Their Relation to Weyl-Wigner Symbols and Symplectic Tomogram Symbols",
volume = "179",
number = "2",
pages = "559-573",
doi = "10.1007/s11232-014-0162-1"
}

Andreev, V. A., Davidović, L. D., Davidović, M. D., Davidović, M. D., Manko, 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, 179(2), 559-573.
https://doi.org/10.1007/s11232-014-0162-1

Andreev VA, Davidović LD, Davidović MD, Davidović MD, Manko 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, V. A., Davidović, Ljubica D., Davidović, Milena D., Davidović, Miloš D., Manko, 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 . .