Coherent Collective Excitations in a Superfluid: Spontaneously Broken Symmetries and Fluctuations-Dissipation
Abstract
Description
This paper presents an elementary theory of the phase-coherent collective excitations in both He II in the gravitational field and atomic Bose-Einstein condensation in a trap. The theory is based on the concept of off-diagonal long-range order by Penrose and Onsager and the quantum theory of Bohm, with emphasis on the broken symmetry in a Bose-Einstein gas with repulsive interactions. It is shown that a spontaneously broken symmetry that accompanies a phonon (Nambu-Goldstone mode) takes place at the surface layer of an inhomogeneous Bose system in the presence of an external field. The spontaneously broken symmetry in a Bose system is described and is shown to manifest itself in both He II and the Bose-Einstein condensation - a shell-like structure of Bose-Einstein condensation in a trap. The broken symmetry gives a coherent explanation for a number of long standing puzzles in He II.
84 pages, 1 figure, (1) The Bose-Einstein condensation is discussed in both a degenerate Bose gas and an imperfect Bose gas to show how the pair-interaction affects the nature of phase-transition, (2) The Onsager-Feynman quantization of circulation in He II is discussed with the identifiable cause with Planck's quantum condition
84 pages, 1 figure, (1) The Bose-Einstein condensation is discussed in both a degenerate Bose gas and an imperfect Bose gas to show how the pair-interaction affects the nature of phase-transition, (2) The Onsager-Feynman quantization of circulation in He II is discussed with the identifiable cause with Planck's quantum condition