  We investigate the full functional form of the first passage time density
(FPTD) of a tracer particle in a single-file diffusion (SFD) system whose
population is: (i) homogeneous, i.e., all particles having the same diffusion
constant and (ii) heterogeneous, with diffusion constants drawn from a
heavy-tailed power-law distribution. In parallel, the full FPTD for fractional
Brownian motion [fBm - defined by the Hurst parameter, 0<H<1] is studied, of
interest here as fBm and SFD systems belong to the same universality class.
  Extensive stochastic (non-Markovian) SFD and fBm simulations are performed
and compared to two analytical Markovian techniques: the Method of Images
approximation (MIA) and the Willemski-Fixman approximation (WFA). We find that
the MIA cannot approximate well any temporal scale of the SFD FPTD. Our exact
inversion of the Willemski-Fixman integral equation captures the long-time
power-law exponent, when H >= 1/3, as predicted by Molchan [1999] for fBm. When
H<1/3, which includes homogeneous SFD (H=1/4), and heterogeneous SFD (H<1/4),
the WFA fails to agree with any temporal scale of the simulations and Molchan's
long-time result.
  SFD systems are compared to their fBm counter parts; and in the homogeneous
system both scaled FPTDs agree on all temporal scales including also, the
result by Molchan, thus affirming that SFD and fBm dynamics belong to the same
universality class. In the heterogeneous case SFD and fBm results for
heterogeneity-averaged FPTDs agree in the asymptotic time limit. The
non-averaged heterogeneous SFD systems display a lack of self-averaging. An
exponential with a power-law argument, multiplied by a power-law pre-factor is
shown to describe well the FPTD for all times for homogeneous SFD and
sub-diffusive fBm systems.
