By Carlo F. Barenghi

The goal of this primer is to hide the basic theoretical info, fast and concisely, for you to let 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 choice of the fabric, either concerning the content material and point of presentation, attracts at the authors research of the good fortune of proper examine initiatives with beginners to the sphere, in addition to of the scholars suggestions from many taught and self-study classes at the topic matter.

Starting with a short historic evaluation, this article covers particle facts, weakly interacting condensates and their dynamics and eventually superfluid helium and quantum turbulence.

At the top of every bankruptcy (apart from the 1st) there'll be a few routines. distinctive strategies could be made to be had to teachers upon request to the authors.

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055 × 10−34 Js. When numerically solving the GPE to model a condensate, it would be better if the numbers which we compute were of order unity; this minimises the role of floating point errors which are inherent to modern digital computation. Another problem is that not all the parameters which appear in the GPE are independent: identifying the truly independent parameters reduces the number of numerical simulations which are needed to understand the nature of the solution. It is therefore useful to introduce dimensionless variables and write the GPE in simpler dimensionless form.

The quantity g( p)d p represents the number of states lying between momenta p and p + d p. These states occupy a (6D) volume in phase space which is the product of their (3D) volume in position space and their (3D) volume in momentum space. The former is the box volume, V. For the latter, the range p to p + d p represents a spherical shell in momentum space of inner radius p and thickness d p, as illustrated in Fig. 7, with momentum-space volume 4π p 2 d p. Hence the phase space volume is 4π p 2 Vd p.

Pitaevskii, S. Stringari, Bose-Einstein Condensation (International Series of Monographs on Physics) (Oxford Science Publications, Oxford, 2003) 4. P. Proukakis, B. Jackson, J. Phys. B 41, 203002 (2008) 5. B. S. J. J. W. Gardiner, Adv. Phys. 57, 363 (2008) 6. P. A. Gardiner, M. Davis, M. ), Quantum Gases: Finite Temperature and Non-Equilibrium Dynamics (Imperial College Press, London, 2013) 7. F. Dalfovo, S. P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999) 8. D. W. P. Reinhardt, Phys.

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