# Bose-Einstein Condensation in Dilute Gases by C. J. Pethick, H. Smith

By C. J. Pethick, H. Smith

Pethick and Smith supply a unified creation to the physics of ultracold atomic Bose and Fermi gases for college kids, experimentalists and theorists alike. This ebook explains the phenomena in ultracold gases from simple ideas, with no assuming a close wisdom of atomic, condensed topic, and nuclear physics. This e-book presents chapters to hide the statistical physics of trapped gases, atomic houses, cooling and trapping atoms, interatomic interactions, constitution of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. difficulties are integrated on the finish of every bankruptcy.

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J. Keeling, F. M. Marchetti, M. H. Szymanska, R. Andr´e, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and Le Si Dang, Nature 443, 409 (2006). [27] G. E. Brown, in Ref. [19], p. 438. [28] M. G. Alford, A. Schmitt, K. Rajagopal, and T. 4635, (Rev. Mod. , in press). 2 The non-interacting Bose gas The topic of Bose–Einstein condensation in a uniform, non-interacting gas of bosons is treated in most textbooks on statistical mechanics [1]. In the present chapter we discuss the properties of a non-interacting Bose gas in a trap.

85) for α > 2, disappears when α < 2 by using the identity ∞ N − Cα Γ(α)ζ(α)(kT )α = Cα d α−1 0 1 e( −μ)/kT −1 − 1 e /kT −1 at temperatures just above Tc . 5 Consider a uniform non-interacting gas of N identical bosons of mass m in a volume V . 4 to calculate the chemical potential as a function of temperature and volume at temperatures just above Tc . Show that the speciﬁc heat at constant pressure, Cp , diverges as (T − Tc )−1 when the temperature approaches Tc from above. ] References [1] L.

2 above, where the eﬀect of the potential was included through the density of states. 1). We now consider the density of particles which are not in the condensate. This is given by p (r) nex (r) = = dp (2π )3 e[ 1 p (r)−μ]/kT −1 . 45) by introducing the variable x = p2 /2mkT and the quantity z(r) deﬁned by the equation z(r) = e[μ−V (r)]/kT . 46) For V (r) = 0, z reduces to the fugacity. 47) where λT = (2π 2 /mkT )1/2 is the thermal de Broglie wavelength, Eq. 2). Integrals of this type occur frequently in expressions for properties of ideal Bose gases, so we shall consider a more general one.