By Allan Griffin

The invention of Bose Einstein condensation (BEC) in trapped ultracold atomic gases in 1995 has resulted in an explosion of theoretical and experimental learn at the homes of Bose-condensed dilute gases. the 1st therapy of BEC at finite temperatures, this booklet provides a radical account of the idea of two-component dynamics and nonequilibrium behaviour in superfluid Bose gases. It makes use of a simplified microscopic version to offer a transparent, specific account of collective modes in either the collisionless and collision-dominated areas. significant themes corresponding to kinetic equations, neighborhood equilibrium and two-fluid hydrodynamics are brought at an effortless point. particular predictions are labored out and associated with experiments. supplying a platform for destiny experimental and theoretical reports at the finite temperature dynamics of trapped Bose gases, this ebook is perfect for researchers and graduate scholars in ultracold atom physics, atomic, molecular and optical physics and condensed topic physics.

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**Sample text**

8) corresponds to treating the dynamics of the condensate as if it were moving in a static mean ﬁeld of the noncondensate thermal cloud. One then obtains i¯ h h2 ∇2 ¯ ∂Φ n0 (r) + gnc (r, t) Φ(r, t). 10) There is a considerable literature based on the static thermal cloud in the Popov approximation (m(r, ˜ t) = 0). 10). The self-consistent calculation of these two densities determines the equilibrium properties of the trapped gas within the static Popov approximation. The excitation energies are the quantized ﬂuctuations of the condensate.

1 Generalized GP equation for the condensate Page-33 33 leads to the damping (or growth) of condensate ﬂuctuations. The C12 collisions will play a crucial role in the rest of this book. 2 follows the original approach given by Zaremba et al. (1999). Throughout this chapter (and the whole book), this paper will be referred to as ZNG. The derivation of the collision integrals given in Appendix A of ZNG follows the approach of Kirkpatrick and Dorfman (1985a). We will not repeat this derivation here since the same results are derived in Chapter 6 using the more transparent and systematic Kadanoﬀ–Baym formalism.

Apart from this application, the GP equation was largely unknown. The situation changed overnight in 1995 with the creation of trapped nonuniform Bose condensates in atomic gases. This chapter is a review of the ground state solution of the T = 0 GP equation and of small-amplitude ﬂuctuations (collective oscillations) about this equilibrium state. This review is needed as the starting point for generalizations in the following chapters, which deal with ﬁnite temperatures. 19 BECBook CUP/GFN 20 November 4, 2008 16:42 Page-20 Condensate dynamics at T = 0 For much more detailed accounts of the GP equation at T = 0, we refer to the review by Fetter (1999) as well as the texts by Pethick and Smith (2008) and Pitaevskii and Stringari (2003).