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Conserved Mass Models and Particle Systems in One Dimension | | R. Rajesh
; Satya N. Majumdar
; | | Date: |
14 Oct 1999 | | Journal: | J. Stat. Phys., 99 (2000) 943 | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Abstract: | 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 ($p o 0$ 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 asymmetric continuous mass model, the two limits $p=1$ and $p o 0$ reduce respectively to the $q$-model of force fluctuations in bead packs [S.N. Coppersmith et. al., Phys. Rev. E. {f 53}, 4673 (1996)] and the recently studied asymmetric random average process [J. Krug and J. Garcia, cond-mat/9909034]. We calculate the steady state mass distribution function $P(m)$ assuming product measure and show that it has an algebraic tail for small $m$, $P(m)sim m^{-eta}$ where the exponent $eta$ depends continuously on $p$. For the asymmetric case we find $eta(p)=(1-p)/(2-p)$ for $0leq p <1$ and $eta(1)=-1$ and for the symmetric case, $eta(p)=(2-p)^2/(8-5p+p^2)$ for all $0leq pleq 1$. We discuss the conditions under which the product measure ansatz is exact. We also calculate 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 with distance. | | Source: | arXiv, cond-mat/9910206 | | Services: | Forum | Review | PDF | Favorites | |
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