Atomic Theory of the Two-fluid Model: Broken Gauge Symmetry in Bose-Einstein condensation
Abstract
Description
We discuss the collective excitations in a spatially inhomogeneous (cylindrically symmetric) Bose-Einstein condensation (BEC) at low temperature ($T \ll T_λ$). 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 $ω=c k$, where $k=k_θ=m/r$, the wave number and $c=[4 πa ρ\hbar^{2}]^{1/2}/M$, 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.
20 pages plus one figure
20 pages plus one figure