By C. J. Pethick, H. Smith
In 1925 Einstein envisioned that at low temperatures debris in a gasoline may well all live within the similar quantum nation. This gaseous country, a Bose-Einstein condensate, was once produced within the laboratory for the 1st time in 1995 and investigating such condensates is among the so much energetic parts in modern physics. The authors of this graduate-level textbook clarify this interesting new topic when it comes to easy actual ideas, with no assuming specified earlier wisdom. Chapters conceal the statistical physics of trapped gases, atomic homes, cooling and trapping atoms, interatomic interactions, constitution of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. challenge units also are integrated.
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Extra info for Bose-Einstein condensation in dilute gases
This gives Nex ∼ kT ln min kT . 87) where σ = N/L2 is the number of particles per unit area. The transition temperature is therefore lower by a factor ∼ ln N than the temperature at which the particle spacing is comparable to the thermal de Broglie wavelength. If we take the limit of a large system, but keep the areal density of particles constant, the transition temperature tends to zero. 6 Lower-dimensional systems 37 . Research on spin-polarized hydrogen on surfaces is being pursued at a number of centres, and a review is given in Ref.
47) corresponds to γ = 3/2, and therefore nex (r) = g3/2 (z(r)) . 50) In Fig. 2 we show for a harmonic trap the density of excited particles in units of 1/λ3T for a chemical potential equal to the minimum of the potential. 4 Thermodynamic quantities 29 Fig. 2. The spatial distribution of non-condensed particles, Eq. 50), for an isotropic trap, V (r) = mω02 r2 /2, with R = (2kT /mω02 )1/2 . 49). This gives the distribution of excited particles at the transition temperature or below. 49), is also exhibited for the same value of µ.
64) These results will be used in the discussion of sound modes in Sec. 4. 61) for the speciﬁc heat. 65) while that for the total energy is ∞ E = Cα 1 α d e( −µ)/kT 0 −1 . 66) At high temperatures the mean occupation numbers are small. 68). 19) to express N/Cα in terms of Tc . The speciﬁc heat is then given by C αN k 1 + (α − 1) ζ(α) 2α+1 Tc T α . 70) This approximate form is useful even at temperatures only slightly above Tc . 3 Speciﬁc heat close to Tc Having calculated the speciﬁc heat at high temperatures and at temperatures less than Tc we now determine its behaviour near Tc .