  We study the Zhang model of sandpile on a one dimensional chain of length
$L$, where a random amount of energy is added at a randomly chosen site at each
time step. We show that in spite of this randomness in the input energy, the
probability distribution function of energy at a site in the steady state is
sharply peaked, and the width of the peak decreases as $ {L}^{-1/2}$ for large
$L$. We discuss how the energy added at one time is distributed among different
sites by topplings with time. We relate this distribution to the time-dependent
probability distribution of the position of a marked grain in the one
dimensional Abelian model with discrete heights. We argue that in the large $L$
limit, the variance of energy at site $x$ has a scaling form $L^{-1}g(x/L)$,
where $g(\xi)$ varies as $\log(1/\xi)$ for small $\xi$, which agrees very well
with the results from numerical simulations.
