Peierls instability in pseudo-one-dimensional conductors

We investigate the properties of pseudo-one-dimensional systems which exhibit Peierls instability at $T_c\left(\mu \right)$, where $\mu$ is the Fermi energy as measured from the middle of a conduction band. We show that, except at $\mu =0\mathrm{}$ or $\left|\mu \right|\gg T$, the giant Kohn anomalies of the phonon spectrum do not occur at $2k_F$. For $\left|\mu \right|\ll W$, where $2W$ is the bandwidth, $T_c\left(\mu \right)$ decreases as $\left|\mu \right|$ increases, and, for $W\gg \left|\mu \right|\gg T$, $\frac{T_c\left(\mu \right)}{T_c\mathrm{}\left(0\right)\mathrm{}}=\frac{T_c\mathrm{}\left(0\right)\mathrm{}}{2.26\left|\mu \right|}$. As $\left|\mu \right|$ further increases towards $T_c\left(\mu \right)$, the decrease of $T_c\left(\mu \right)$ towards zero need not in general be monotonic. The neutron scattering differential cross section shows a peak with magnitude proportional to ${(T-T_c)}^{-1\mathrm{}}$.