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 examine at the homes of Bose-condensed dilute gases. the 1st therapy of BEC at finite temperatures, this booklet offers an intensive 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, particular account of collective modes in either the collisionless and collision-dominated areas. significant subject matters similar to kinetic equations, neighborhood equilibrium and two-fluid hydrodynamics are brought at an straight forward point. specific predictions are labored out and associated with experiments. offering a platform for destiny experimental and theoretical reports at the finite temperature dynamics of trapped Bose gases, this publication is perfect for researchers and graduate scholars in ultracold atom physics, atomic, molecular and optical physics and condensed subject physics.

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N ˆ = const. 55) i This transformation shows how the noncondensate part of Hamiltonian can be reduced to a system of noninteracting quasiparticles with a spectrum identical to that of the condensate fluctuations. This equivalence is easy to understand. 7). Standard linear response theory gives (schematically) ˆ HSB ] δΦ ∼ [ψ, ∼ ˜ ψ˜† ] η + [ψ, ˜ ψ] ˜ η∗ . 2 Bogoliubov equations for condensate fluctuations Page-31 31 This shows that the single-particle Green’s functions of the noncondensate fields have the same spectrum as δΦ.

BECBook CUP/GFN November 4, 2008 16:42 Page-19 2 Condensate dynamics at T = 0 Trapped Bose-condensed atomic gases are remarkable because, in spite of the fact that these are very dilute systems, they exhibit robust coherent dynamic behaviour when perturbed. These quantum “wisps of matter” are a new phase of highly coherent matter. While binary collisions are very infrequent, the large coherent mean field associated with the Bose condensate ensures that interactions play a crucial role in determining the collective response of these trapped superfluid gases.

As discussed by these authors, such measurements require an assessment of many experimental complications, including how the number of atoms in the trap changes with temperature. In Fig. 1, we show time-of-flight data from Gerbier et al. 7 Hz. Figure. 60) in three different approximations. The curves give the results for (a) a noninteracting Bose gas (broken line), (b) the TF approximation keeping only the condensate HF mean field (dotted line) and (c) the TF approximation keeping the full HF mean field (solid line).

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