By Carlo F. Barenghi
The goal of this primer is to hide the basic theoretical details, speedy and concisely, for you to permit senior undergraduate and starting graduate scholars to take on tasks in topical learn 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 luck of suitable learn tasks with novices 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 ancient evaluate, this article covers particle facts, weakly interacting condensates and their dynamics and at last superfluid helium and quantum turbulence.
At the tip of every bankruptcy (apart from the 1st) there'll be a few workouts. specified suggestions will be made on hand to teachers upon request to the authors.
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Additional resources for A Primer on Quantum Fluids
Sample text
6 Particle-Wave Overlap Bose–Einstein condensation occurs when N > Nc , with Nc given by Eq. 17). It is equivalent to write this criterion in terms of the number density of particles, n = N /V, as, 3 (2πmkB T )3/2 n>ζ . 21) 2 h3 According to de Broglie, particles behave like waves, with a wavelength λdB = h/ p. h . EmployFor a thermally-excited gas, the particle wavelength is λdB = √ 2πmkB T ing this, the above criterion becomes, nλ3dB > ζ 3 . 22) Upon noting that the average inter-particle distance d = n − 3 and ζ( 23 ) 3 ∼ 1 we arrive at, 1 λdB d.
Note how the distribution changes with N . What form do you expect the distribution to tend towards as N is increased to much larger values? 3 Consider an ideal gas of bosons in two dimensions, confined within a twodimensional box of volume V2D . (a) Derive the density of states g(E) for this two-dimensional system. (b) Using this result show that the number of particles can be expressed as, 30 2 Classical and Quantum Ideal Gases Nex = 2πmV2D kB T h2 ∞ 0 ze−x d x, 1 − ze−x where z = eμ/kB T and x = E/kB T .
Preuss. Akad. Wiss. 3 (1925) References 31 6. P. Pitaevskii, S. Stringari, Bose-Einstein Condensation (International Series of Monographs on Physics) (Oxford Science Publications, Oxford, 2003) 7. J. M. Fairbank, The nature of the lambda-transition in liquid helium, in Progress in Low Temperature Physics, vol. 3, ed. J. 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.
