Geodesic
Free energy of a~many-boson system at low temperatures
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 1, pp. 101-113

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The reduction of operators in the representation of collective variables to self-adjoint form is considered. The Hamiltonian and flux density operator of a many-boson system are reduced explicitly to self-adjoint form. For the obtained Hamiltonian, a perturbation theory is constructed in which each successive term contains, compared with the previous term, an extra sum over the wave vector. The free energy of a system of interacting Bose particles is calculated in the approximation of “two sums over the wave vectors”. From the free energy the internal energy is calculated, being represented as a quadratic functional of the mean population numbers of the elementary excitations. At the same time, the temperature-dependent correction to the Bogolyubov energy spectrum of the elementary excitations is obtained. 
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     author = {I. A. Vakarchuk and P. A. Glushak},
     title = {Free energy of a~many-boson system at low temperatures},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {75},
     number = {1},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_1_a8/}
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I. A. Vakarchuk; P. A. Glushak. Free energy of a~many-boson system at low temperatures. Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 1, pp. 101-113. http://geodesic.mathdoc.fr/item/TMF_1988_75_1_a8/