Condensed Matter Physics, 2010, vol. 13, No. 2, p. 23002:16
DOI:10.5488/CMP.13.23002
Title: Asymptotic exactness of cnumber
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 cnumber for the k=0
mode operator â_{0} 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: BoseEinstein condensation, Bogolyubov's
Hamiltonian, superfluidity, cnumber substitution
PACS: 05.30.Jp, 03.75.Fi, 67.40.w
