An approach is proposed to obtain an effective Hamiltonian of a harmonically trapped Bose-system. Such a Hamiltonian is quadratic in the creation–annihilation operators and certain approximations allow to simplify higher (three and four operator) products to the required form. After the Hamiltonian diagonalization, the expression for the excitation spectrum is obtained containing in particular temperature-dependent corrections. Numerical calculations are made for a one-dimensional system. Some prospects towards the extension of the suggested approach to study binary bosonic mixtures are briefly discussed.
References
1.
M. H.
Anderson
, J. N.
Ensher
, M. R.
Matthews
, C. E.
Wieman
, and E. A.
Cornell
, Science
269
, 198
(1995
).2.
K. B.
Davis
, M.
Mewes
, M. R.
Andrews
, N. J.
van Druten
, D. S.
Durfee
, D. M.
Kurn
, and W.
Ketterle
, Phys. Rev. Lett.
75
, 3969
(1995
).3.
D. S.
Jin
, J. R.
Ensher
, M. R.
Matthews
, C. E.
Wieman
, and E. A.
Cornell
, Phys. Rev. Lett.
77
, 420
(1996
).4.
S.
Stringari
, Phys. Rev. Lett.
77
, 2360
(1996
).5.
L.
You
, W.
Hoston
, M.
Lewenstein
, and M.
Marinescu
, Acta Phys. Pol., A
93
, 211
(1998
).6.
S.
Grossmann
and M.
Holthaus
, Phys. Lett. A
208
, 188
(1995
).7.
H.
Haugerud
, T.
Haugset
, and F.
Ravndal
, Phys. Lett. A
225
, 18
(1997
).8.
W. J.
Mullin
, J. Low Temp. Phys.
106
, 615
(1997
).9.
F.
Gerbier
, Europhys. Lett.
66
, 771
(2004
).10.
A. S.
Parkins
and D. F.
Walls
, Phys. Rep.
303
, 1
(1998
).11.
F.
Dalfovo
, S.
Giorgini
, L. P.
Pitaevskii
, and S.
Stringari
, Rev. Mod. Phys.
71
, 463
(1999
).12.
I.
Bloch
, J.
Dalibard
, and W.
Zwerger
, Rev. Mod. Phys.
80
, 885
(2008
).13.
V. S.
Bagnato
, D. J.
Frantzeskakis
, P. G.
Kevrekidis
, B. A.
Malomed
, and D.
Mihalache
, Rom. Rep. Phys.
67
, 5
(2015
).14.
C.
Menotti
and S.
Stringari
, Phys. Rev. A
66
, 043610
(2002
).15.
Y.-W.
Luo
and J.-S.
Chen
, Commun. Theor. Phys.
60
, 673
(2013
).16.
K. R. A.
Hazzard
and E. J.
Mueller
, Phys. Rev. A
76
, 063612
(2007
).17.
M.
Yamashita
, S.
Kato
, A.
Yamaguchi
, S.
Sugawa
, T.
Fukuhara
, S.
Uetake
, and Y.
Takahashi
, Phys. Rev. A
87
, 041604(R)
(2013
).18.
I. V.
Stasyuk
, O. V.
Velychko
, and I. R.
Dulepa
, Ukr. J. Phys.
59
, 993
(2014
).19.
20.
P.
Grech
and R.
Seiringer
, Commun. Math. Phys.
322
, 559
(2013
).21.
R.
Seiringer
, J. Math. Phys.
55
, 075209
(2014
).22.
C.
Trallero-Giner
, M. V.
Durnev
, Y.
Núñez Fernández
, M. I.
Vasilevskiy
, V.
López-Richard
, and A.
Kavokin
, Phys. Rev. B
89
, 205317
(2014
).23.
V. I.
Yukalov
and H.
Kleinert
, Phys. Rev. A
73
, 063612
(2006
).24.
T.
Ernst
, T.
Paul
, and P.
Schlagheck
, Phys. Rev. A
81
, 013631
(2010
).25.
V. I.
Yukalov
, E. P.
Yukalova
, and V. S.
Bagnato
, Laser Phys.
19
, 686
(2009
).26.
V. I.
Yukalov
, Phys. Part. Nucl.
42
, 460
(2011
).27.
N.
Argaman
and Y. B.
Band
, Phys. Rev. A
83
, 023612
(2011
).28.
A.
Alastuey
and J.
Piasecki
, Phys. Rev. E
84
, 041122
(2011
).29.
H.
Kim
, C. S.
Kim
, C. L.
Huang
, H.-S.
Song
, and X.-X.
Yi
, Phys. Rev. A
85
, 033611
(2012
).30.
H.
Kim
, C.-S.
Kim
, C.-L.
Huang
, H.-S.
Song
, and X.-X.
Yi
, Phys. Rev. A
85
, 053629
(2012
).31.
A.
Roy
and D.
Angom
, Phys. Rev. A
92
, 011601
(2015
).32.
X.-L.
Chen
, Y.
Li
, and H.
Hu
, Phys. Rev. A
91
, 063631
(2015
).33.
A. A.
Rovenchak
, J. Low Temp. Phys.
148
, 411
(2007
).34.
J. H. P.
Colpa
, Physica A
93
, 327
(1978
).35.
C.
Tsallis
, J. Math. Phys.
19
, 277
(1978
).36.
M.
Marinescu
and A. F.
Starace
, Phys. Rev. A
56
, 570
(1997
).37.
38.
39.
R. D.
Lord
, J. London Math. Soc.
s1-24
, 101
(1949
).40.
41.
S.
Giorgini
, L. P.
Pitaevskii
, and S.
Stringari
, Phys. Rev. A
54
, R4633
(1996
).42.
K.
Kasamatsu
and M.
Tsubota
, J. Low Temp. Phys.
150
, 599
(2008
).43.
R.
Campbell
, G.-L.
Oppo
, and M.
Borkowski
, Phys. Rev. E
91
, 012909
(2015
).44.
B.
Pasquiou
, A.
Bayerle
, S. M.
Tzanova
, S.
Stellmer
, J.
Szczepkowski
, M.
Parigger
, R.
Grimm
, and F.
Schreck
, Phys. Rev. A
88
, 023601
(2013
).45.
B.
Van Schaeybroeck
, Physica A
392
, 3806
(2013
).© 2016 AIP Publishing LLC.
2016
AIP Publishing LLC
You do not currently have access to this content.