Scale Transformations in Phase Space and Stretched States of a Harmonic Oscillator
Samo za registrovane korisnike
2017
Autori
Andreev, V. A.Davidović, Dragomir M.
Davidović, Ljubica D.
Davidović, Milena D.
Davidović, Miloš D.
Članak u časopisu (Objavljena verzija)
Metapodaci
Prikaz svih podataka o dokumentuApstrakt
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.
Ključne reči:
phase space / Husimi function / scale transformation / harmonic oscillator / stretched state / uncertainty relationIzvor:
Theoretical and Mathematical Physics, 2017, 192, 1, 1080-1096Finansiranje / projekti:
- Fizičke implikacije modifikovanog prostor-vremena (RS-MESTD-Basic Research (BR or ON)-171031)
- Novi pristup problemima zasnivanja kvantne mehanike sa aspekta primene u kvantnim tehnologijama i interpretacijama signala različitog porekla (RS-MESTD-Basic Research (BR or ON)-171028)
- Serbian Ministry of Education, Science, and Technological Development
DOI: 10.1134/S0040577917070091
ISSN: 0040-5779; 1573-9333
WoS: 000407759300009
Scopus: 2-s2.0-85027407589
Institucija/grupa
VinčaTY - 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 . .