  We study the dynamics of a tagged particle in an environment of point
Brownian particles with hard-core interactions in an infinite one dimensional
channel (a single-file model). In particular we examine the influence of
initial conditions on the dynamic of the tagged particle. We compare two
initial conditions: equal distances between particles and uniform density
distribution. The effect is shown by the differences of
mean-square-displacement and correlation function for the two ensembles of
initial conditions. We discuss the violation of Einstein relation, and its
dependence on the initial condition, and the difference between time and
ensemble averaging. More specifically, using the Jepsen line, we will discuss
how transport coefficients, like diffusivity, depend on the initial state. Our
work shows that initial conditions determine the long time limit of the
dynamic, and in this sense the system never forgets its initial state in
complete contrast with thermal systems (i.e a closed system which attains
equilibrium independent of the initial state).
