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

Abstract

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.