By Carlo F. Barenghi
The objective of this primer is to hide the basic theoretical details, fast and concisely, so that it will allow senior undergraduate and starting graduate scholars to take on initiatives in topical study parts of quantum fluids, for instance, solitons, vortices and collective modes.
The number of the cloth, either concerning the content material and point of presentation, attracts at the authors research of the good fortune of correct study tasks with newbies 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 assessment, this article covers particle information, 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. unique suggestions could be made to be had to teachers upon request to the authors.
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Additional info for A Primer on Quantum Fluids
Statistical weighting W ? . ? Cell energy E 6 5 .. 2 Consider a system with N classical particles distributed over 3 cells (labelled 1, 2, and 3) of energy 0, and 2 . 5N . (a) Obtain an expression for the number of microstates in terms of N and N3 , the population of cell 3. (b) Plot the number of microstates as a function of N2 (which parameterises the macrostate) for N = 50. Repeat for N = 100 and 500. 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?
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 .
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. The application of the normalization condition, Eq. 2), to the above solution and manipulation of the resulting expression leads to useful relations for the chemical potential and the energy of the condensate in terms of the number of atoms N , μ= ωr 2 15N as r 2/5 , E= 5 μN .
A Primer on Quantum Fluids by Carlo F. Barenghi