Atomic Theory of the Two-fluid Model: Broken Gauge Symmetry in Bose-Einstein condensation

Details Atomic Theory of the Two-fluid Model: Broken Gauge Symmetry in Bose-Einstein condensation Atomic Theory of the Two-fluid Model: Broken Gauge Symmetry in Bose-Einstein condensation

2005-09-14

arxiv.org/abs/cond-mat/0509350v1

Physics

Condensed Matter

Other Condensed Matter

20 pages plus one figure

Scientific paper

We discuss the collective excitations in a spatially inhomogeneous (cylindrically symmetric) Bose-Einstein condensation (BEC) at low temperature ($T \ll T_{\lambda}$). The main result is the dispersion relation for a (first) sound wave that is obtained by describing the perturbation as a Lagrangian coordinate. The dispersion curve is in good agreement with the Bogoliubov phonon spectrum $\omega=c k$, where $k=k_{\theta}=m/r$, the wave number and $c=[4 \pi a \rho \hbar^{2}]^{1/2}/M$, the speed of first sound. Based on Bohm's quantum theory, a spontaneously broken gauge symmetry in a quantum fluid is discussed in terms of the quantum fluctuation-dissipation, from which it is shown that the symmetry breaking takes place at the free surface of BEC in an external field.

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