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Y. Castin, in edited by M. Inguscio, W. Ketterle, and C. Salomon (SIF, Rome
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Y. Castin, in Lecture Notes of the 2006 Varenna Enrico Fermi School on Fermi Gases, edited by, M. Inguscio,,, W. Ketterle,, and, C. Salomon, (SIF, Rome, 2007).
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Fluctuations of the number of particles within a given volume in cold quantum gases
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in edited by R. Kaiser, C. Westbrook, and F. David (EDP Sciences and Springer-Verlag, Berlin
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Landau, L.1
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77953196952
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′). Using polar coordinates we obtain I = 1 2 √ α β arctan β - α 2 √ α β. For β > α this is also I = 1 √ α β [π 4 - 1 2 arctan 2 √ α β β - α] = 1 √ α β [π 4 - arctan √ α β]
-
′). Using polar coordinates we obtain I = 1 2 √ α β arctan β - α 2 √ α β. For β > α this is also I = 1 √ α β [π 4 - 1 2 arctan 2 √ α β β - α] = 1 √ α β [π 4 - arctan √ α β].
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13
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77953206110
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/2(1-lηx2)]Πα(1+lηα2). This result is qualitatively incorrect: It depends on ωy and ωz, whereas the exact expression (13) does not. It is quantitatively incorrect even in the isotropic case, where cLDA~(1/2)/ηx for ηx→0, to be compared to (21).
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/2 (1 - l η x 2)] Π α (1 + l η α 2). This result is qualitatively incorrect: It depends on ω y and ω z, whereas the exact expression (13) does not. It is quantitatively incorrect even in the isotropic case, where c LDA ~ (1 / 2) / η x for η x → 0, to be compared to (21).
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15
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0006712406
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PYLAAG 0375-9601 10.1016/0375-9601(95)00766-V
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/2/3], where S is a sum involving Bernoulli numbers B2k, S=k≥1Γ(2k-3/2)B2k/(2k)!0.1461. On the other hand, using (i) the integral representation of the Riemann ζ function, see §9.512 with q=1 in Gradshteyn and Ryzhik [, Academic Press, San Diego
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/2 ζ (- 1 / 2) / π.
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77953199169
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)-rr), but this does not affect the result due to symmetry reasons.
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)-rr), but this does not affect the result due to symmetry reasons.
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4644328584
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Atom interferometry with a weakly interacting bose-einstein condensate
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The accuracy of the Bogoliubov approximation to calculate the pair distribution function was checked by exact quantum Monte Carlo calculations for a trapped gas [24].
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The accuracy of the Bogoliubov approximation to calculate the pair distribution function was checked by exact quantum Monte Carlo calculations for a trapped gas [24].
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42749104313
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note
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*= v j, we obtain δ ρ j = ψ 0 (u j + v j) and δ S / = (u j - v j) / (2 i ψ 0). For real mode functions the normalization condition u j 2 - v j 2 = 1 together with Euler's equation - i ε j δ S j / = - g δ ρ j gives the normalization condition 2 g ε j U (r) < μ d 3 r δ ρ j 2 = 1. Let us consider for simplicity the isotropic case (see, e.g., [S. Sinha and Y. Castin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87. 190402 87, 190402 (2001)] for the general anisotropic case). In the hydrodynamic approximation, δ ρ is a product of a polynomial P (r / R), where R is the Thomas-Fermi radius, a spherical harmonic and a normalization factor N j. The coefficients of the polynomial are numbers that were calculated in
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4243160819
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[, PRLTAO 0031-9007 10.1103/PhysRevLett.77.2360
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[S. Stringari, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77. 2360 77, 2360 (1996)]. We then find that N j 2 scales as ε j / (gR 3) so that the matrix element squared | s (x) (| u j + | v j ) | 2 scales as ε j / μ. On the other hand, nj k B T / ε j for the low-frequency modes. We then find the scaling c class k B T / μ.
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Stringari, S.1
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77953220517
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-1η=j(1/ εj)[(|vj|uj)(\uj|,vj|)+(|uj*|vj*)(vj*|,j*|)] with η=(100-1), see, e.g., Ref. [22].
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-1η=j(1/ εj)[(|vj|uj)(\uj|,vj|)+(|uj*|vj*)(vj*|,j*|)] with η=(100-1), see, e.g., Ref. [22].
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|