-
1
-
-
11944274056
-
-
M. H. Anderson, J. R. Enscher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science 269, 198 (1995)
-
(1995)
Science
, vol.269
, pp. 198
-
-
Anderson, M.H.1
Enscher, J.R.2
Matthews, M.R.3
Wieman, C.E.4
Cornell, E.A.5
-
2
-
-
4244115335
-
-
K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Phys. Rev. Lett. 75, 3969 (1995)
-
(1995)
Phys. Rev. Lett.
, vol.75
, pp. 3969
-
-
Davis, K.B.1
Mewes, M.-O.2
Andrews, M.R.3
van Druten, N.J.4
Durfee, D.S.5
Kurn, D.M.6
Ketterle, W.7
-
3
-
-
4243132347
-
-
Phys. Rev. Lett.C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, 75, 1687 (1995)
-
(1995)
Phys. Rev. Lett.
, vol.75
, pp. 1687
-
-
Bradley, C.C.1
Sackett, C.A.2
Tollett, J.J.3
Hulet, R.G.4
-
5
-
-
0033246313
-
-
F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys. 71, 463 (1999).
-
(1999)
Rev. Mod. Phys.
, vol.71
, pp. 463
-
-
Dalfovo, F.1
Giorgini, S.2
Pitaevskii, L.P.3
Stringari, S.4
-
9
-
-
0000724476
-
-
S. T. Beliaev, Zh. Eksp. Teor. Fiz. 34, 433 (1958) [Sov. Phys. JETP 7, 299 (1958)]
-
(1958)
Sov. Phys. JETP
, vol.7
, pp. 299
-
-
Beliaev, S.T.1
-
12
-
-
0002428394
-
-
reprinted in The Many-Body Problem, edited by D. Pines (W. A. Benjamin, New York, 1961)
-
N. N. Bogoliubov, J. Phys. (Moscow) 11, 23 (1947),reprinted in The Many-Body Problem, edited by D. Pines (W. A. Benjamin, New York, 1961).
-
(1947)
J. Phys. (Moscow)
, vol.11
, pp. 23
-
-
Bogoliubov, N.N.1
-
16
-
-
85036361238
-
-
e-print cond-mat/9807120
-
A. Yu. Cherny, e-print cond-mat/9807120.
-
-
-
Yu. Cherny, A.1
-
18
-
-
85036370288
-
-
It is not, of course, the case at nonzero temperatures when spatial boson correlations occur even in the absence of any interaction. Nevertheless, this difference between the zero- and nonzero-temperature situations does not influence the fact that (Formula presented) is connected with the scattering parts of the pair wave functions (3)
-
It is not, of course, the case at nonzero temperatures when spatial boson correlations occur even in the absence of any interaction. Nevertheless, this difference between the zero- and nonzero-temperature situations does not influence the fact that (Formula presented) is connected with the scattering parts of the pair wave functions (3).
-
-
-
-
19
-
-
85036397050
-
-
By the leading order in (Formula presented) we mean zero depletion of the condensate: (Formula presented)
-
By the leading order in (Formula presented) we mean zero depletion of the condensate: (Formula presented).
-
-
-
-
25
-
-
85036331480
-
-
This can always be achieved with a global gauge transformation of the Bose operators (Formula presented) and (Formula presented) provided there are no magnetic fields (see, e.g., Ref. 8
-
This can always be achieved with a global gauge transformation of the Bose operators (Formula presented) and (Formula presented) provided there are no magnetic fields (see, e.g., Ref. 8).
-
-
-
-
26
-
-
85036341239
-
-
Using formula (5.12) of the paper of Hugenholtz and Pines 4 together with the relations (4.4) of the paper of Beliaev 4, for (Formula presented) one can derive (Formula presented) where (Formula presented) is the Fourier transform of (Formula presented) and (Formula presented). So, using the definition of the structure factor, one can arrive at (Formula presented) for (Formula presented). Here for (Formula presented) we have (Formula presented), which can be rewritten in the form of Eq. (9)
-
Using formula (5.12) of the paper of Hugenholtz and Pines 4 together with the relations (4.4) of the paper of Beliaev 4, for (Formula presented) one can derive (Formula presented) where (Formula presented) is the Fourier transform of (Formula presented) and (Formula presented). So, using the definition of the structure factor, one can arrive at (Formula presented) for (Formula presented). Here for (Formula presented) we have (Formula presented), which can be rewritten in the form of Eq. (9).
-
-
-
-
28
-
-
85036421894
-
-
We stress that the potential is involved through the mediation of the scattering length (11) only in the first few terms in the low-density expansions. For the high-order terms the dependence on a specific shape of the potential should appear
-
We stress that the potential is involved through the mediation of the scattering length (11) only in the first few terms in the low-density expansions. For the high-order terms the dependence on a specific shape of the potential should appear.
-
-
-
-
29
-
-
85036228805
-
-
The Bogoliubov model, which is in fact perturbation theory with respect to the coupling constant (Formula presented), provides accuracy up to the last term in Eq. (42) proportional to (Formula presented) 22. For this reason, in the expansion (42) there is no (Formula presented) term proportional to (Formula presented)
-
The Bogoliubov model, which is in fact perturbation theory with respect to the coupling constant (Formula presented), provides accuracy up to the last term in Eq. (42) proportional to (Formula presented) 22. For this reason, in the expansion (42) there is no (Formula presented) term proportional to (Formula presented).
-
-
-
-
30
-
-
36149018678
-
-
T. T. Wu, Phys. Rev. 115, 1390 (1959).
-
(1959)
Phys. Rev.
, vol.115
, pp. 1390
-
-
Wu, T.T.1
-
31
-
-
85036166846
-
-
V. V. Tolmachev, Dokl. Akad. Nauk. (SSSR) 135, 41 (1960) [ Sov. Phys. Dokl. 5, 1190 (1960)].
-
(1960)
Sov. Phys. Dokl.
, vol.5
, pp. 1190
-
-
Tolmachev, V.V.1
-
32
-
-
85036149224
-
-
For example, this can be shown as follows. For a strongly singular potential (Formula presented) for (Formula presented) we have (Formula presented) and (Formula presented), which in conjunction with Eqs. (3) and (4) leads to (Formula presented) and (Formula presented). So (Formula presented)
-
For example, this can be shown as follows. For a strongly singular potential (Formula presented) for (Formula presented) we have (Formula presented) and (Formula presented), which in conjunction with Eqs. (3) and (4) leads to (Formula presented) and (Formula presented). So (Formula presented).
-
-
-
-
33
-
-
85036141414
-
-
Note that Eq. (67) can help to derive the strong-coupling generalization of the Gross-Pitaevskii equation on a solid theoretical basis beyond any effective-interaction picture
-
Note that Eq. (67) can help to derive the strong-coupling generalization of the Gross-Pitaevskii equation on a solid theoretical basis beyond any effective-interaction picture.
-
-
-
|