  The effects of noise in particle-in-cell (PIC) and Vlasov simulations of the
Buneman instability in unmagnetized plasmas are studied. It is found that, in
the regime of low drift velocity, the linear stage of the instability in PIC
simulations differs significantly from the theoretical predictions, whereas in
the Vlasov simulations it does not. A series of highly resolved PIC simulations
with increasingly large numbers of macroparticles per cell is performed using a
number of different PIC codes.
  All the simulations predict highly similar growth rates that are several
times larger than those calculated from the linear theory. As a result, we find
that the true convergence of the PIC simulations in the linear regime is
elusive to achieve in practice and can easily be misidentified.
  The discrepancy between the theoretical and observed growth rates is
attributed to the initial noise inherently present in PIC simulations, but not
in Vlasov simulations, that causes particle trapping even though the fraction
of trapped particles is low. We show analytically that even weak distortions of
the electron velocity distribution function (such as flattening due to particle
trapping) result in significant modifications of the growth rates. It is also
found that the common quiet-start method for PIC simulations leads to more
accurate growth rates but only if the maximum growth rate mode is perturbed
initially. We demonstrate that the quiet-start method does not completely
remedy the noise problem because the simulations generally exhibit
inconsistencies with the linear theory.
