Abstract
The mixtures of quantum degenerate Bose and Fermi gases in highly anisotropic traps at zero temperature are studied. It is found that under some conditions the system becomes unstable with respect to the spontaneous formation of the collective mode with wave vector 2 k F ( k F is a Fermi wave vector) by exploring the Bogoliubov phonon spectrum. This type of instability is the analogue of Peierls instability in quasi-one-dimensional conductors.
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