Conserved mass models and particle systems in one dimension

In this paper we study analytically a simple one-dimensional model of mass transport. We introduce a parameter p that interpolates between continuous- time dynamics (p --> limit) and discrete parallel update dynamics (p = 1). For each p, we study the model with (i) both continuous and discrete masses and (ii) both symmetric and asymmetric transport of masses. In the asymmet ric continuous mass model, the two limits p = 1 and p --> 0 reduce respecti vely to the q-model of force fluctuations in bead packs [S. N. Coppersmith ei al., Phys. Rev. E 53:4673 (1996)] and the recently studied asymmetric ra ndom average process [J. Krug and J. Garcia, cond-mat/9909034]. We calculat e the steady-stale mass distribution function P(m) assuming product measure and show that it has an algebraic tail for small m, P(m) similar to m(-bet a) where the exponent beta depends continuously on p. For the asymmetric ca se we find beta(p) = (1 - p)/(2 - p) for 0 less than or equal to p < 1 and beta(1) = -1, and for the symmetric case, beta(p) = (2 - p)(2)/(8 - 5p + p( 2)) for all 0 less than or equal to p less than or equal to 1. We discuss t he conditions under which the product measure ansatz is exact. We also calc ulate exactly the steady-state mass-mass correlation function and show that while it decouples in the asymmetric model, in the symmetric case it has a nontrivial spatial oscillation with an amplitude decaying exponentially wi th distance.