  In this article, we present a simulation study of the linear and nonlinear
spectroscopy of dense atomic vapors. Motivated by recent experiments, we focus
on double quantum spectroscopy which directly probes dipole-dipole
interactions. By including explicitly thermal velocity, we show that
temperature has an important impact on the self-broadening mechanism of the
linear and nonlinear spectra. We also provide analytical expressions for the
response functions in the short time limit using the two-body approximation
which shows that double quantum spectroscopy for atomic vapors directly probes
the transition amplitude of the electronic excitation between two atoms. We
also propose an expression for the double quantum spectrum that includes the
effect of Doppler broadening and we discuss the effect of density on the
spectrum. We show that when Doppler broadening is negligible compared to
self-broadening the double quantum spectrum scales with the atomic density
while when Doppler broadening dominates it scales as the square of the density.
