By Carlo F. Barenghi
The objective of this primer is to hide the fundamental theoretical info, fast and concisely, so that it will let senior undergraduate and starting graduate scholars to take on initiatives in topical learn parts of quantum fluids, for instance, solitons, vortices and collective modes.
The number 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 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 ancient assessment, this article covers particle records, 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 workouts. distinct strategies will be made to be had to teachers upon request to the authors.
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Extra info for A Primer on Quantum Fluids
The harmonic trap was spherically-symmetric with with ωr = 1130 Hz. Calculate the critical temperature according to the ideal Bose gas prediction. 5 × 1018 m−3 ). 6 The compressibility β of a gas, a measure of how much it shrinks in response to a compressional force, is defined as, β=− 1 ∂V . V ∂P Determine the compressibility of the ideal gas for T < Tc . Hint: Since Tc is a function of V, you should ensure the full V-dependence is present before differentiating. References 1. 2. 3. 4. 5. F. Mandl, Statistical Physics, 2nd edn.
However, the complexity of this approach makes it intractable for modelling more than a few particles, let alone the thousands or millions typical of an atomic BEC. Fortunately, the interactions in atomic BECs are weak; this is due to their extreme diluteness and the weak forces between neutral atoms. As such, quantum fluctuations have a weak effect on the condensate, and will be ignored. Then, and assuming a large number of particles (N 1), the many-body wavefunction can be approximated by an effective single-particle wavefunction, Ψ (r, t).
The quantity ground harmonic oscillator wavefunction ψ(r ) = mω π 2 |ψ(r )| represents the probability of finding the particle at position r . For a condensate 1, the particle density profile will follow as, of N0 such particles, with N0 5 Box-like traps [8, 9] are also possible, and allow the condensate to have uniform density, facilitating comparison with the theory of homogeneous condensates. 26 2 Classical and Quantum Ideal Gases Fig. 12 Variation of condensate fraction N0 /N with temperature for a harmonically-trapped BEC, with the ideal-gas predictions (solid line) compared to experimental measurements from Ref.
A Primer on Quantum Fluids by Carlo F. Barenghi