By Carlo F. Barenghi
The goal of this primer is to hide the basic theoretical info, speedy and concisely, to be able 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 choice of the fabric, either in regards to the content material and point of presentation, attracts at the authors research of the good fortune of suitable 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 assessment, 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. certain options may be made to be had to teachers upon request to the authors.
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Extra info for A Primer on Quantum Fluids
7, with momentum-space volume 4π p 2 d p. Hence the phase space volume is 4π p 2 Vd p. Now recall that each quantum state takes up a volume h 3 in phase space. Thus the number of states between p and p + d p is, g( p)d p = 4π p 2 V d p. 12) Using the momentum-energy relation p 2 = 2m E, its differential form d p = √ m/2E dE), and the relation g(E) dE = g( p) d p, Eq. 12) leads to, 3 2π(2m) 2 V 1 g(E) = E2. 13) This is the density of states for an ideal gas confined to a box of volume V. There are a diminishing amount of states in the limit of zero energy, and an increasing amount with larger energy.
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. Rev. A 62, 063610 (2000) 9. D. W. P. Reinhardt, Phys. Rev. A 62, 063611 (2000) Chapter 4 Waves and Solitons Abstract In the previous chapter we considered the shape of steady state condensates, either homogeneous or confined by trapping potentials.
4 The three most common condensate shapes that can be formed in an axisymmetric harmonic potential: a a cigar condensate (ωx , ω y > ωz ), b a spherical condensate (ωx = ω y = ωz ), and c a pancake condensate (ωx , ω y < ωz ) than the condensate energy scale (the chemical potential, μ), then excitations of the condensate in the x and y directions are highly suppressed, and the only significant dynamics occur in the z direction. The system has become effectively one-dimensional. An effectively two-dimensional condensate can be realized for ωz and ωz μ.