DYNAMICS OF BOSE-EINSTEIN CONDENSATE WITH ACCOUNT OF PAIR CORRELATIONS
Keywords:
Bose-Einstein condensate, anomalous and normal averages, pair correlations, sound branch of elementary excitations, elementary excitations with energy gap
Abstract
It is shown that for the system of Bose particles it can be obtained the chain of equations for the quasiaverages of the products of field operators, being similar to the Bogolyubov-Born-Green-Kirkwood-Yvon chain in the theory of classical gases. For the case when it is sufficient to confine ourselves to taking account of the quasiaverages of only one field operator and the products of two field operators, the closed system of dynamic equations for Bose-Einstein condensate at zero temperature is obtained which accounts for the one-particle condensate and pair correlations. A spatially homogeneous state in the absence of the external field is considered and the spectrum of small oscillations of the condensate in this case with account of pair correlations is explored. It is shown that the spectrum of collective excitations has two branches: the sound wave branch and the branch with an energy gap at zero momentum. he first of the branches approaches the Bogolyubov spectrum at low momenta, and the second branch – at large momenta. It is discussed the possibility of existence of the quasiparticle excitations with an energy gap in the superfluid helium in connection with the experiment on the absorption of microwave radiation.
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References
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3. Pitaevskii L., Stringari S. Bose-Einstein condensation. – Oxford University Press USA, 2003.
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6. Bogolyubov N.N. Problems of dynamic theory in statistical physics / Selected works in three volumes. – Kiev: Naukova Dumka. – 1970. – Vol. 2. – P. 522.
7. Peletminskii A.S., Peletminskii S.V., Poluektov Yu.M. Role of single-particle and pair condensates in Bose systems with arbitrary intensity of interaction // Condensed Matter Physics, 2013, vol. 16, No. 1, 13603. arXiv:1303.5539 [cond-mat.statmech].
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9. Poluektov Yu.M. On self-consistent determination of the quasi-average in statistical physics // Low Temp. Phys. – 1997 – Vol. 23. – No.9. – P. 685; [FNT. – 1997 – Vol. 23. – No.9. – P. 915-922].
10. Aziz R.A., Slaman. M.J. An examination of ab initio result for the helium potential energy curve // J. Chem. Phys. – 1991 –Vol. 94. – P. 8047.
11. Anderson J.B., Traynor C.A., Boghosian B.M. An exact quantum Monte Carlo calculation of the helium-helium intermolecular potential // J. Chem. Phys. – 1993 – Vol. 99 – P. 345.
12. Brueckner K. A. Theory of nuclear structure. The many body problem. – London: Methuen a.o., 1959.
13. Bogolyubov N.N. On the theory of superfluidity // J. Phys. USSR – 1946 – Vol. 11 – P. 23-32.; [Izv. AN SSSR, Ser. Fiz – 1947 – Vol. 11. – No. 1. – P. 77-90.]
14. Bogolyubov N.N., Bogolyubov N.N. (Jr). Introduction to quantum statistical mechanics. – Moscow: Nauka, 1984. – 384p.
15. Poluektov Yu.M. Pro kvantovopol'ovyi opys bagatochastynkovych Boze-system zі spontanno porushenymy symetrіyamy [About quantum field description of many particle Bose - systems with spontaneously broken symmetry] // UFZh. – 2007. – Vol. 52. – No.6. – P. 578-594 [arXiv.org cond-mat arXiv: 1306.2103]. (in Ukrainian)
16. Poluektov Yu.M. A simple model of Bose–Einstein condensation of interacting particles // JLTP. – 2017 – Vol. 186. – No.5-6. – P. 347-362.
17. Bijl A. The lowest wave function of the symmetrical many particles system // Physica – 1940 – Vol. 7 – P.869-886.
18. Girardeau M., Arnowitt R. Theory of many-boson system: pair theory // Phys. Rev. – 1959. – Vol.113. – No.3. – P. 755-761.
19. Wentzel G. Thermodynamically equivalent Hamiltonian for some many-body problems // Phys. Rev. – 1960. – Vol.120. – No. 5. – P. 1572-1575.
20. Luban M. Statistical mechanics of a nonideal boson gas: pair Hamiltonian model // Phys. Rev. – 1962. – Vol.128 – No.2. – P. 965-987.
21. Tolmachev V.V. Temperature elementary excitations in a non-ideal Bose-Einstein system // DAN SSSR – 1960 – Vol.135 – No. 4. – P. 825-828. (in Russian)
22. Poluektov Yu.M. Self-consistent field model for spatially inhomogeneous Bose systems // Low Temperature Physics. – 2002. – Vol. 28. – No.6. – P. 429-441; [FNT – 2002. – Vol. 28. – No.6. – P. 604-620].
23. Rybalko A., Rubets S., Rudavskii E., Tikhiy V., Tarapov S., Golovashchenko R., Derkach V. Resonance absorption of microwaves in HeII: Evidence for roton emission // Phys. Rev. B. – 2007. – Vol.76. – P.140503.
24. Poluektov Yu.M. Absorption of electromagnetic field energy by the superfluid system of atoms with a dipole moment // Low Temperature Physics. – 2014. – Vol. 40. – No.5. – P. 389; [FNT – 2014. – Vol. 40. – No.5 – P. 503-512].
Published
2017-08-01
Cited
How to Cite
Poluektov, Y. M., & Arslanaliev, A. M. (2017). DYNAMICS OF BOSE-EINSTEIN CONDENSATE WITH ACCOUNT OF PAIR CORRELATIONS. East European Journal of Physics, 4(2), 29-36. https://doi.org/10.26565/2312-4334-2017-2-04
Section
Original Papers
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