Peierls instability, periodic Bose-Einstein condensates, and density waves in quasi-one-dimensional boson-fermion mixtures of atomic gases

We study the quasi-one-dimensional (Q1D) spin-polarized Bose-Fermi mixture of atomic gases at zero temperature. Bosonic excitation spectra are calculated in the random phase approximation on the ground state with uniform Bose-Einstein condensates (BEC's) and the Peierls instabilities are shown to appear in bosonic collective excitation modes with wave number 2kF by the coupling between the Bogoliubov-phonon mode of bosonic atoms and the fermion particle-hole excitations. The ground-state properties are calculated in the variational method, and, corresponding to the Peierls instability, the state with a periodic BEC and fermionic density waves with the period π/kF are shown to have a lower energy than the uniform one. We also briefly discuss the Q1D system confined in a harmonic oscillator potential and derive the Peierls instability condition for it