Teoreticheskaya i Matematicheskaya Fizika, 1971, Volume 6, Number 1, Pages 90–108(Mi tmf3409)
This article is cited in 10 scientific papers (total in 10 papers)
Application of functional integration to the derivation of the low-frequency asymptotic behaviour of Green's functions and kinetic equations for a nonideal Bose gas
Abstract:
A form of perturbation theory is developed which enables one to calculate the Green's functions
of a nonideal Bose gas below the Bose condensation point for low energies and momenta
(in the hydrodynamic region). The functional integral method is used to find the diagrams
of perturbation theory that make the main contribution to the hydrodynamic asymptotic behavior
of the Green's functions. It is shown that summation of these diagrams reduces to solution
of kinetic-type equations. The solution of these equations by the Chapman–Enskog–Hilbert method in the first approximation gives the Green's functions with poles corresponding
to first and second sound. The second approximation enables one to express the damping
in terms of the transport coefficients of first and second viscosity and the thermal conductivity.
These coefficients are determined by the collision integral, which is obtained automatically
in the process of summation of the diagrams.
Citation:
V. N. Popov, “Application of functional integration to the derivation of the low-frequency asymptotic behaviour of Green's functions and kinetic equations for a nonideal Bose gas”, TMF, 6:1 (1971), 90–108; Theoret. and Math. Phys., 6:1 (1971), 65–77
This publication is cited in the following 10 articles:
D. D. Solnyshkov, C. Leblanc, S. V. Koniakhin, O. Bleu, G. Malpuech, “Quantum analogue of a Kerr black hole and the Penrose effect in a Bose-Einstein condensate”, Phys. Rev. B, 99:21 (2019)
Stoof H.T.C., van Heugten J. J. R. M., “Resummation of Infrared Divergencies in the Theory of Atomic Bose Gases”, J. Low Temp. Phys., 174:3-4 (2014), 159–183
J Saliba, P Lugan, V Savona, “Superfluid–insulator transition in weakly interacting disordered Bose gases: a kernel polynomial approach”, New J. Phys., 15:4 (2013), 045006
R. Graham, D. F. Walls, M. J. Collett, M. Fliesser, E. M. Wright, “Collapses and revivals of collective excitations in trapped Bose condensates”, Phys. Rev. A, 57:1 (1998), 503
S. V. Peletminskii, A. I. Sokolovsky, V. S. Shchelokov, “Hydrodynamics of a superfluid bose liquid with allowance for dissipative processes in a model with weak interaction”, Theoret. and Math. Phys., 34:1 (1978), 51–61
V. S. Kapitonov, V. N. Popov, “Hydrodynamic action for a plasma”, Theoret. and Math. Phys., 26:2 (1976), 164–170
V. A. Andrianov, V. N. Popov, “Hydrodynamic action and Bose spectrum of superfluid Fermi systems”, Theoret. and Math. Phys., 28:3 (1976), 829–837
V. N. Popov, “Hydrodynamic Hamiltonian for a nonideal Bose gas”, Theoret. and Math. Phys., 11:2 (1972), 478–486
V. N. Popov, “On the theory of the superfluidity of two- and one-dimensional bose systems”, Theoret. and Math. Phys., 11:3 (1972), 565–573
I. M. Khalatnikov, V. L. Pokrovskii, D. M. Semiz, “High-frequency hydrodynamics near the ? point”, J Low Temp Phys, 6:3-4 (1972), 305
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