  (000, 000)(00, 00) (-00, 000)[(a)]{} (00, 000)[(b)]{} (-00, 00)[(c)]{} (00, 00)[(d)]{} (-00, 00)[![\[fig:-0\](Color Online) (a) Dispersion relation $\omega^0(k)$ for various values of $q$ using $^{00}$Rb parameters ($c_{0} < 0$) at $T= 0\mu$K and $n_{0} = 00^{00}$cm$^{-0}$: q=0 (solid, black), $q = 0|c_{0}|n_{0}$ (blue, dashed), $q = 0|c_{0}|n_{0}$ (green, dotted), $q = 0.0|c_{0}|n_{0}$ (red, thin). (b) Gapless, linear dispersion for small $k$ at $q = 0|c_{0}|n_{0}$. The solid black curve is the small $k$ expansion (\[eq:0\]). (c) $q = 0|c_{0}|n_{0}$ dispersion in detail. The horizontal black line is $\omega^{0} = q(q - 0|c_{0}|n_{0})$, which is the gap predicted by the small $k$ expansion (\[eq:0\]). (d) $q=0$ dispersion in detail. Horizontal dashed line at $\omega^{0} = -0c^{0}_{0}n^{0}_{0}$ indicates the most unstable mode. Vertical dotted line is at $k\Lambda_{T} = \frac{\sqrt{0 |c_{0}|c_{0}}n_{0}}{k_{B} T}$.](fig0.eps "fig:")]{} (00, 00)[![\[fig:-0\](Color Online) (a) Dispersion relation $\omega^0(k)$ for various values of $q$ using $^{00}$Rb parameters ($c_{0} < 0$) at $T= 0\mu$K and $n_{0} = 00^{00}$cm$^{-0}$: q=0 (solid, black), $q = 0|c_{0}|n_{0}$ (blue, dashed), $q = 0|c_{0}|n_{0}$ (green, dotted), $q = 0.0|c_{0}|n_{0}$ (red, thin). (b) Gapless, linear dispersion for small $k$ at $q = 0|c_{0}|n_{0}$. The solid black curve is the small $k$ expansion (\[eq:0\]). (c) $q = 0|c_{0}|n_{0}$ dispersion in detail. The horizontal black line is $\omega^{0} = q(q - 0|c_{0}|n_{0})$, which is the gap predicted by the small $k$ expansion (\[eq:0\]). (d) $q=0$ dispersion in detail. Horizontal dashed line at $\omega^{0} = -0c^{0}_{0}n^{0}_{0}$ indicates the most unstable mode. Vertical dotted line is at $k\Lambda_{T} = \frac{\sqrt{0 |c_{0}|c_{0}}n_{0}}{k_{B} T}$.](fig0.eps "fig:")]{} (-00, 00)[![\[fig:-0\](Color Online) (a) Dispersion relation $\omega^0(k)$ for various values of $q$ using $^{00}$Rb parameters ($c_{0} < 0$) at $T= 0\mu$K and $n_{0} = 00^{00}$cm$^{-0}$: q=0 (solid, black), $q = 0|c_{0}|n_{0}$ (blue, dashed), $q = 0|c_{0}|n_{0}$ (green, dotted), $q = 0.0|c_{0}|n_{0}$ (red, thin). (b) Gapless, linear dispersion for small $k$ at $q = 0|c_{0}|n_{0}$. The solid black curve is the small $k$ expansion (\[eq:0\]). (c) $q = 0|c_{0}|n_{0}$ dispersion in detail. The horizontal black line is $\omega^{0} = q(q - 0|c_{0}|n_{0})$, which is the gap predicted by the small $k$ expansion (\[eq:0\]). (d) $q=0$ dispersion in detail. Horizontal dashed line at $\omega^{0} = -0c^{0}_{0}n^{0}_{0}$ indicates the most unstable mode. Vertical dotted line is at $k\Lambda_{T} = \frac{\sqrt{0 |c_{0}|c_{0}}n_{0}}{k_{B} T}$.](fig0.eps "fig:")]{} (00, 00)[![\[fig:-0\](Color Online) (a) Dispersion relation $\omega^0(k)$ for various values of $q$ using $^{00}$Rb parameters ($c_{0} < 0$) at $T= 0\mu$K and $n_{0} = 00^{00}$cm$^{-0}$: q=0 (solid, black), $q = 0|c_{0}|n_{0}$ (blue, dashed), $q = 0|c_{0}|n_{0}$ (green, dotted), $q = 0.0|c_{0}|n_{0}$ (red, thin). (b) Gapless, linear dispersion for small $k$ at $q = 0|c_{0}|n_{0}$. The solid black curve is the small $k$ expansion (\[eq:0\]). (c) $q = 0|c_{0}|n_{0}$ dispersion in detail. The horizontal black line is $\omega^{0} = q(q - 0|c_{0}|n_{0})$, which is the gap predicted by the small $k$ expansion (\[eq:0\]). (d) $q=0$ dispersion in detail. Horizontal dashed line at $\omega^{0} = -0c^{0}_{0}n^{0}_{0}$ indicates the most unstable mode. Vertical dotted line is at $k\Lambda_{T} = \frac{\sqrt{0 |c_{0}|c_{0}}n_{0}}{k_{B} T}$.](fig0.eps "fig:")]{} (-00, 00