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We investigate the full functional form of the first passage time density(FPTD) of a tracer particle in a single-file diffusion (SFD) system whosepopulation is: (i) homogeneous, i.e., all particles having the same diffusionconstant and (ii) heterogeneous, with diffusion constants drawn from aheavy-tailed power-law distribution. In parallel, the full FPTD for fractionalBrownian motion [fBm - defined by the Hurst parameter, 0<H<1] is studied, ofinterest here as fBm and SFD systems belong to the same universality class.  Extensive stochastic (non-Markovian) SFD and fBm simulations are performedand compared to two analytical Markovian techniques: the Method of Imagesapproximation (MIA) and the Willemski-Fixman approximation (WFA). We find thatthe MIA cannot approximate well any temporal scale of the SFD FPTD. Our exactinversion of the Willemski-Fixman integral equation captures the long-timepower-law exponent, when H >= 1/3, as predicted by Molchan [1999] for fBm. WhenH<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'slong-time result.  SFD systems are compared to their fBm counter parts; and in the homogeneoussystem both scaled FPTDs agree on all temporal scales including also, theresult by Molchan, thus affirming that SFD and fBm dynamics belong to the sameuniversality class. In the heterogeneous case SFD and fBm results forheterogeneity-averaged FPTDs agree in the asymptotic time limit. Thenon-averaged heterogeneous SFD systems display a lack of self-averaging. Anexponential with a power-law argument, multiplied by a power-law pre-factor isshown to describe well the FPTD for all times for homogeneous SFD andsub-diffusive fBm systems.

First Passage Times for a Tracer Particle in Single File Diffusion and Fractional Brownian Motion