Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2005-05-16
Physics
Condensed Matter
Other Condensed Matter
total 16 pages, including 1 figure
Scientific paper
A theory of collective excitations in Bose-Einstein condensation in a trap is developed based on the quantum Hamilton-Jacobi equation of Bohm and the phase coherence along with the idea of off-diagonal long range order of Penrose and Onsager. First, we show that a free surface behaves like a normal fluid - a breakdown of superfluidity. Second, inside the free surface it is shown that the spectrum of phonons is of the form $\omega=ck$ scaled with the external potential, where the speed of (first) sound, $c=[4\pi a\rho\hbar^{2}]^{1/2}/M$ and $k$ is the wave number. Third, in the limit $a\to 0$, the hard spheres in the Bose-Einstein condensation collapse to a close-packed classical lattice with the zero-point vibrational motion about fixed points.
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