Title: Asymptotic exactness of c-number substitution in Bogolyubov's theory of superfluidity
Author(s):

	N.N. Bogolyubov, Jr. (V.A. Steklov Institute of Mathematics, Gubkin Str. 8, Moscow, 119991, Russia) ,
	D.P. Sankovich (V.A. Steklov Institute of Mathematics, Gubkin Str. 8, Moscow, 119991, Russia)

The Bogolyubov model of liquid helium is considered. The validity of substituting a c-number for the k=0 mode operator â₀ is established rigorously. The domain of stability of the Bogolyubov's Hamiltonian is found. We derive sufficient conditions which ensure the appearance of the Bose condensate in the model. For some temperatures and some positive values of the chemical potential, there is a gapless Bogolyubov spectrum of elementary excitations, leading to a proper microscopic interpretation of superfluidity.

Key words: Bose-Einstein condensation, Bogolyubov's Hamiltonian, superfluidity, c-number substitution
PACS: 05.30.Jp, 03.75.Fi, 67.40.-w

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