Quintessence and tachyon dark energy models with a constant equation of
  state parameter
  In this work we determine the correspondence between quintessence and tachyon
dark energy models with a constant dark energy equation of state parameter,
$w_e$. Although the evolution of both the Hubble parameter and the scalar field
potential with redshift is the same, we show that the evolution of
quintessence/tachyon scalar fields with redshift is, in general, very
different. We explicity demonstrate that if $w_e \neq -1$ the potentials need
to be very fine-tuned for the relative perturbation on the equation of state
parameter, $\Delta w_e/(1+w_e) \ll 1$, to be very small around the present
time. We also discuss possible implications of our results for the
reconstruction of the evolution of $w_e$ with redshift using varying couplings.
