By A. Griffin, D. W. Snoke, S. Stringari

This booklet is dedicated to BEC as an interdisciplinary topic, overlaying atomic and molecular physics, laser physics, low temperatures, and astrophysics, and it'll function an in-depth record on fresh development and may recommend promising examine issues for graduate scholars and researchers in physics.

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**Additional info for Bose-Einstein Condensation**

**Sample text**

I will only quote the results at absolute zero. In the unperturbed ground state, the total density n is equal to that of the condensate no = No/SI. When perturbations are turned on, the condensate is depleted, due to both the hard-sphere interactions and to the random potentials. The total density is thus made up of three terms: n = n 0 + m + n R, (37) where n\ arises from the hard-sphere interactions, and can be read off (31), while nR arises from the random potentials: Bose-Einstein Condensation and Superfluidity 45 ni = .

The latter energy contains a kinetic part due to localization of the particles, and a potential energy Va corresponding to the lattice spacing a N ma2 Because the repulsive potential V(r) decreases with r, we have Va < Vm. It follows that the crystalline state will be favoured for strong coupling (it optimizes the potential energy), while the Bose condensed liquid will win at weak coupling (it minimizes the kinetic energy). An obvious example is 4He, which is a superfluid at low pressure and which freezes at higher densities.

30) The sound velocity deduced from the Bogoliubov quasiparticle spectrum is c = (h/m)y/4nan£9 which agrees with that calculated via the compressibility by differentiating Eo. Bose-Einstein Condensation and Superfluidity 41 The condensate density is defined by no = n — Q~l Sk^ ground state, which corresponds to £ = 1, we have This shows that the interactions deplete the Bose condensate; but the superfluidity density at absolute zero is n, from Khalatnikov's formula (17). The partition sum should extend over all values of £.