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 TMF, 1972, Volume 11, Number 3, Pages 354–365 (Mi tmf2875)

On the theory of the superfluidity of two- and one-dimensional bose systems

V. N. Popov

Abstract: A hydrodynamic Hamiltonian for two- and one-dimensional Bose systems is constructed by the method of functional integration. Its form indicates that there is superfluidity and two- fluid hydrodynamics at low temperatures despite the absence of a condensate. This result is clear from the fact that the single-particle Green's functions decrease at large distances in accordance with a power law in two-dimensional systems if $T\ne0$ and in one-dimensional systems if $T=0$, while they decrease exponentially in one-dimensional systems if $T\ne0$. A model is calculated for a two-dimensional low-density Bose gas; the thermodynamic functions and the equation of the phase transition curve are found. It is shown that allowance for quantum vortices in a two-dimensional Bose system does not alter the power-law decrease of the Green's functions at large distances.

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English version:
Theoretical and Mathematical Physics, 1972, 11:3, 565–573

Citation: V. N. Popov, “On the theory of the superfluidity of two- and one-dimensional bose systems”, TMF, 11:3 (1972), 354–365; Theoret. and Math. Phys., 11:3 (1972), 565–573

Citation in format AMSBIB
\Bibitem{Pop72} \by V.~N.~Popov \paper On the theory of the superfluidity of two- and one-dimensional bose systems \jour TMF \yr 1972 \vol 11 \issue 3 \pages 354--365 \mathnet{http://mi.mathnet.ru/tmf2875} \transl \jour Theoret. and Math. Phys. \yr 1972 \vol 11 \issue 3 \pages 565--573 \crossref{https://doi.org/10.1007/BF01028373} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. N. Popov, “Theory of one-dimensional Bose gas with point interaction”, Theoret. and Math. Phys., 30:3 (1977), 222–226
2. N. M. Bogolyubov, A. G. Izergin, V. E. Korepin, “Critical exponents in completely integrable models of quantum statistical physics”, Theoret. and Math. Phys., 70:1 (1987), 94–102
3. A. V. Zabrodin, A. A. Ovchinnikov, “Single-particle density matrix of a one-dimensional system of spin 1/2 Fermi particles”, Theoret. and Math. Phys., 85:3 (1990), 1321–1325
4. N. M. Bogolyubov, K. L. Malyshev, “Functional integration and the twopoint correlation function of the one-dimensional Bose-gas in the harmonic potential”, St. Petersburg Math. J., 17:1 (2006), 63–84
5. N. M. Bogolyubov, K. L. Malyshev, “On the calculation of the asymptotics of the two-point correlation function of the one-dimensional Bose gas in the trapping potential”, J. Math. Sci. (N. Y.), 151:2 (2008), 2829–2839
6. Werner F., Castin Y., “General Relations for Quantum Gases in Two and Three Dimensions: Two-Component Fermions”, Phys. Rev. A, 86:1 (2012), 013626
7. Pustilnik M. Matveev K.A., “Fate of Classical Solitons in One-Dimensional Quantum Systems”, Phys. Rev. B, 92:19 (2015), 195146
8. Salasnich L., “Goldstone and Higgs Hydrodynamics in the Bcs-Bec Crossover”, Condens. Matter, 2:2 (2017), UNSP 22
9. Martone G.I., Larre P.-E., Fabbri A., Pavloff N., “Momentum Distribution and Coherence of a Weakly Interacting Bose Gas After a Quench”, Phys. Rev. A, 98:6 (2018), 063617
10. M. M. Glazov, R. A. Suris, “Collective states of excitons in semiconductors”, Phys. Usp., 63:11 (2020), 1051–1071
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