By Carlo F. Barenghi
The target of this primer is to hide the fundamental theoretical info, fast and concisely, so as to permit senior undergraduate and starting graduate scholars to take on initiatives in topical examine parts of quantum fluids, for instance, solitons, vortices and collective modes.
The collection of the fabric, either concerning the content material and point of presentation, attracts at the authors research of the good fortune of correct study tasks with beginners to the sector, in addition to of the scholars suggestions from many taught and self-study classes at the topic matter.
Starting with a short old review, this article covers particle data, weakly interacting condensates and their dynamics and at last superfluid helium and quantum turbulence.
At the top of every bankruptcy (apart from the 1st) there'll be a few workouts. special suggestions could be made on hand to teachers upon request to the authors.
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Extra resources for A Primer on Quantum Fluids
3 Energy E (in units of N ωr ) versus σ according to Eq. 5, 1]. 67 (dashed line) marks the critical point for the onset of collapse the local minimum shifts to smaller widths; the attractive interactions cause the condensate to become narrower and more peaked. However, beyond some critical attractive interactions, the local minimum disappears and no stable solutions exist. In other words, all states collapse to zero width. 64. This tendency to collapse is the reason why repulsive condensates are more common and why we have avoided discussing condensates with attractive interactions so far.
Gorter (North Holland, Amsterdam, 1961) 8. L. F. Schmidutz, I. P. Smith, Z. Hadzibabic, Phys. Rev. Lett. 110, 200406 (2013) 9. L. , Nat. Comm. 6, 6162 (2015) 10. R. S. R. E. A. Cornell, Phys. Rev. Lett. 77, 4984 (1996) 11. A. S. Rokhsar, Phys. Rev. A 55, 4346 (1997) 12. F. London, Nature 141, 643 (1938) Chapter 3 Gross-Pitaevskii Model of the Condensate Abstract The Gross-Pitaevskii equation (GPE) is a successful and well-established model for describing an atomic Bose-Einstein condensate. Here we introduce this model, along with its assumptions.
27) Substituting n = |ψ|2 and V (r ) = 21 mω 2 r 2 , we obtain n(r ) = (2μ − mωr2 r 2 )/2g. Density cannot be negative, so we assume that n(r ) = 0 if 2μ ≤ mωr2 r 2 . The last equality defines the Thomas-Fermi radius Rr , which satisfies, μ= 1 mωr2 Rr2 . 29) 1, the Thomasand has the shape of an inverted parabola. Provided that N as / r Fermi solution is an excellent approximation of the solution of the GPE determined numerically, and compares well with experimental data, as shown in Fig. 2. Note, however, the slight deviation from the true numerical solution close to the condensate’s edge; here the gradient terms, neglected within the Thomas-Fermi model, become significant.