By Carlo F. Barenghi
The goal of this primer is to hide the fundamental theoretical info, speedy and concisely, for you to permit senior undergraduate and starting graduate scholars to take on tasks in topical learn components 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 luck of proper examine tasks with novices 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 statistics, 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. particular recommendations may be made on hand to teachers upon request to the authors.
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Extra resources for A Primer on Quantum Fluids
33) All states are occupied up to an energy threshold E F , termed the Fermi energy (equal to the T = 0 chemical potential). 13). Note that the continuum approximation N = g(E) N (E) dE holds for N 1 fermions since the unit occupation of the ground state is always negligible. Rearranging for the Fermi energy in terms of the particle density n = N /V gives, EF = 2 2m 6π 2 n 2/3 . 35) From this we define the Fermi momentum pF = kF where kF = (6π 2 n)1/3 is the Fermi wavenumber. In momentum space, all states are occupied up to momentum pF , termed the Fermi sphere.
We can also deduce the density profile of the thermal gas. Taking the classical limit, the atoms will be distributed over energy according to the Boltzmann distribution N (E) ∝ e−E/kB T . 32) where r,th = 2kB T /mωr2 characterises the width of the thermal gas and the profile has been normalized to Nex atoms. For increased temperature, the atoms have higher average energy and climb further up the trap walls, leading to a wider profile. While the profiles of the ideal condensate and ideal thermal gas are both Gaussian in space, their widths have different functional forms.
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