  We compute the spectral function $A({\bf k}, \omega)$ of a model
two-dimensional high-temperature superconductor, at both zero and finite
temperatures $T$. We assume that an areal fraction $c_{\beta}$ of the
superconductor has a large gap $\Delta$ ($\beta$ regions), while the rest has a
smaller $\Delta$ ($\alpha$ regions), both of which are randomly distributed in
space. We find that $A({\bf k}, \omega)$ is most strongly affected by
inhomogeneity near the point $\mathbf k = (\pi, 0)$ (and the symmetry-related
points). For $c_\beta\simeq 0.5$, $A({\bf k}, \omega)$ exhibits two double
peaks (at positive and negative energy) near this k-point if the difference
between $\Delta_\alpha$ and $\Delta_\beta$ is sufficiently large in comparison
to the hopping integral. The strength of the inhomogeneity required to produce
a split spectral function peak suggests that inhomogeneity is unlikely to be
the cause of a second branch in the dispersion relation. Thermal fluctuations
also affect $A({\bf k}, \omega)$ most strongly near $\mathbf k = (\pi,0)$.
Typically, peaks that are sharp at $T = 0$ become reduced in height, broadened,
and shifted toward lower energies with increasing $T$; the spectral weight near
$\mathbf k = (\pi, 0)$ becomes substantial at zero energy for $T$ greater than
the phase-ordering temperature.

Superconductivity;Mesoscale and Nanoscale Physics