We calculate the one-body temperature Greens (Matsubara) function of the unitary Fermi gas via Quantum Monte Carlo, and extract the spectral weight function $A(p,omega)$ using the methods of maximum entropy and singular value decomposition. From $A(p
,omega)$ we determine the quasiparticle spectrum, which can be accurately parametrized by three functions of temperature: an effective mass $m^*$, a mean-field potential $U$, and a gap $Delta$. Below the critical temperature $T_c=0.15varepsilon_F$ the results for $m^*$, $U$ and $Delta$ can be accurately reproduced using an independent quasiparticle model. We find evidence of a pseudogap in the fermionic excitation spectrum for temperatures up to {$T^*approx 0.20varepsilon_{F} > T_c$}.
A unitary Fermi gas has a surprisingly rich spectrum of large amplitude modes of the pairing field alone, which defies a description within a formalism involving only a reduced set of degrees of freedom, such as quantum hydrodynamics or a Landau-Ginz
burg-like description. These modes are very slow, with oscillation frequencies well below the pairing gap, which makes their damping through quasiparticle excitations quite ineffective. In atomic traps these modes couple naturally with the density oscillations, and the corresponding oscillations of the atomic cloud are an example of a new type of collective mode in superfluid Fermi systems. They have lower frequencies than the compressional collective hydrodynamic oscillations, have a non-spherical momentum distribution, and could be excited by a quick time variation of the scattering length.
