Titlebook: Vortices in Bose-Einstein Condensates; Amandine Aftalion Book 2006 Birkh?user Boston 2006 Potential.condensed matter.mathematical modeling

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The Mathematical Setting: A Survey of the Main Theorems,mi regime; double-scale convergence, homogenization techniques, and Fock-Bargmann space for the fast-rotating regime; energy estimates and nondegeneracy of a solution for the superfluid flow. The main mathematical results are summarized in the present chapter.

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The Mathematical Setting: A Survey of the Main Theorems,(Chapters 3, 4, 6); the fast-rotation regime, which displays a vortex lattice (Chapter 5); and the experiment of a superfluid flow around an obstacle (Chapter 7). The tools and techniques needed to address these problems are very different: energy expansion using a small parameter for the Thomas-Fer

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Two-Dimensional Model for otating Condensate,ter, and Ω is the given rotational velocity. We assume that ρTF(.)= ρ0 ?r. . is the disc of radius R.= √ρ0 in . (so that ρTF = 0 on ?., and ∫. ρTF = 1, which prescribes the value of ρ0. The issue is to determine the number and location of vortices according to the value of Ω.

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Other Trapping Potentials,?ū)/2, ε is a small parameter, and Ω is the given rotational velocity. We assume that D = {ρTF > 0} and ρTF(.) describes respectively a nonradial harmonic confinement and a quartic trapping potential, that is, the model case are .In case (4.3), for certain values of . and ., the domain . becomes an

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Book 2006een observed by rotating the trap holding the atoms. In contrast to a classical fluid for which the equilibrium velocity corresponds to solid body rotation, a quantum fluid such as a Bose–Einstein condensate can rotate only through the nucleation of quantized vortices. This monograph is dedicated to